prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What factors control the reliance of artificial organisms on plasticity?

Read the following text and answer briefly.

Context 1: Paper Info

Title: Environmental variability and network structure determine the optimal plasticity mechanisms in embodied agents
Publish Date: Unkown
Author List: Sina Khajehabdollahi (from Department of Computer Science, University of Tübingen)

Figure

Figure2: An outline of the network controlling the foraging agent The sensor layer receives inputs at each time step (the ingredients of the nearest food), which are processed by the plastic layer in the same way as the static sensory network, Fig 1 The output of that network is given as input to the motor network, along with the distance d and angle α to the nearest food, the current velocity v, and energy E of the agent These signals are processed through two hidden layers to the final output of motor commands as the linear and angular acceleration of the agent
Figure4: The evolved parameters θ = (θ 1 ,      , θ 8 ) of the plasticity rule for the reward prediction (a ) and the decision (b ) tasks, for a variety of parameters (p tr = 0 01, d e ∈ 0, 0 1,      , 1, and σ ∈ 0, 0 1,      , 1 in all 100 combinations) Despite the relatively small difference between the tasks, the evolved learning rules differ considerably For visual guidance, the lines connect θs from the same run 
Figure5: a The trajectory of an agent (blue line) in the 2D environment A well-trained agent will approach and consume food with positive values (green dots) and avoid negative food (red dots) b The learning rate of the plastic sensory network eta p grows with the distance between environments d e c  and decreases with the frequency of environmental change d The fitness of an agent (measured as the total food consumed over its lifetime) increases over generations of the EA for both the scalar and binary readouts in the sensory network e The Pearson correlation coefficient of an evolved agent's weights with the ingredient value vector of the current environment (E 1 -blue, E 2 -red) In this example, the agent's weights are anti-correlated with its environment, which is not an issue for performance since the motor network can interpret the inverted signs of food 

abstract

The evolutionary balance between innate and learned behaviors is highly intricate, and different organisms have found different solutions to this problem  We hypothesize that the emergence and exact form of learning behaviors is naturally connected with the statistics of environmental fluctuations and tasks an organism needs to solve 
Here, we study how different aspects of simulated environments shape an evolved synaptic plasticity rule in static and moving artificial agents  We demonstrate that environmental fluctuation and uncertainty control the reliance of artificial organisms on plasticity  Interestingly, the form of the emerging plasticity rule is additionally determined by the details of the task the artificial organisms are aiming to solve 
Moreover, we show that coevolution between static connectivity and interacting plasticity mechanisms in distinct sub-networks changes the function and form of the emerging plasticity rules in embodied agents performing a foraging task  One of the defining features of living organisms is their ability to adapt to their environment and incorporate new information to modify their behavior 
It is unclear how the ability to learn first evolved , but its utility appears evident  Natural environments are too complex for all the necessary information to be hardcoded genetically and more importantly, they keep changing during an organism's lifetime in ways that cannot be anticipated ;   The link between learning and environmental uncertainty and fluctuation has been extensively demonstrated in both natural ; , and artificial environments  
Nevertheless, the ability to learn does not come without costs  For the capacity to learn to be beneficial in evolutionary terms, a costly nurturing period is often required, a phenomenon observed in both biological , and artificial organisms   Additionally, it has been shown that in some complex environments, hardcoded behaviors may be superior to learned ones given limits in the agent's lifetime and envi-ronmental uncertainty ; ;  
The theoretical investigation of the optimal balance between learned and innate behaviors in natural and artificial systems goes back several decades  However, it has recently found also a wide range of applications in applied AI systems ;   Most AI systems are trained for specific tasks, and have no need for modification after their training has been completed 
Still, technological advances and the necessity to solve broad families of tasks make discussions about life-like AI systems relevant to a wide range of potential application areas  Thus the idea of open-ended AI agents that can continually interact with and adapt to changing environments has become particularly appealing 
Many different approaches for introducing lifelong learning in artificial agents have been proposed  Some of them draw direct inspiration from actual biological systems ;   Among them, the most biologically plausible solution is to equip artificial neural networks with some local neural plasticity , similar to the large variety of synaptic plasticity mechanisms ; ; that performs the bulk of the learning in the brains of living organisms  
The artificial plasticity mechanisms can be optimized to modify the connectivity of the artificial neural networks toward solving a particular task  The optimization can use a variety of approaches, most commonly evolutionary computation  The idea of meta-learning or optimizing synaptic plasticity rules to perform specific functions has been recently established as an engineering tool that can compete with stateof-the-art machine learning algorithms on various complex tasks ; ; Pedersen and Risi (2021);  
Additionally, it can be used to reverse engineer actual plasticity mechanisms found in biological neural networks and uncover their functions ;   Here, we study the effect that different factors (environ-arXiv:2303 06734v1 [q-bio NC] 12 Mar 2023 mental fluctuation and reliability, task complexity) have on the form of evolved functional reward-modulated plasticity rules 
We investigate the evolution of plasticity rules in static, single-layer simple networks  Then we increase the complexity by switching to moving agents performing a complex foraging task  In both cases, we study the impact of different environmental parameters on the form of the evolved plasticity mechanisms and the interaction of learned and static network connectivity 
Interestingly, we find that different environmental conditions and different combinations of static and plastic connectivity have a very large impact on the resulting plasticity rules  We imagine an agent who must forage to survive in an environment presenting various types of complex food particles  Each food particle is composed of various amounts and combinations of N ingredients that can have positive (food) or negative (poison) values 
The value of a food particle is a weighted sum of its ingredients  To predict the reward value of a given resource, the agent must learn the values of these ingredients by interacting with the environment  The priors could be generated by genetic memory, but the exact values are subject to change  To introduce environmental variability, we stochastically change the values of the ingredients 
More precisely, we define two ingredient-value distributions E 1 and E 2 and switch between them, with probability p tr for every time step  We control how (dis)similar the environments are by parametrically setting E 2 = (1 − 2d e )E 1 , with d e ∈ [0, 1] serving as a distance proxy for the environments; when d e = 0, the environment remains unchanged, and when d e = 1 the value of each ingredient fully reverses when the environmental transition happens 
For simplicity, we take values of the ingredients in E 1 equally spaced between -1 and 1 (for the visualization, see Fig  )  The static agent receives passively presented food as a vector of ingredients and can assess its compound value using the linear summation of its sensors with the (learned or evolved) weights, see Fig   
The network consists of N sensory neurons that are projecting to a single post-synaptic neuron  At each time step, an input X t = (x 1 ,       , x N ) is presented, were the value x i , i ∈ {1,       , N } represents the quantity of the ingredient i  We draw x i independently form a uniform distribution on the [0, 1] interval (x i ∼ U (0, 1)) 
The value of each ingredient w c i is determined by the environment (E 1 or E 2 )  The postsynaptic neuron outputs a prediction of the food X t value as y t = g(W X T t )  Throughout the paper, g will be either the identity function, in which case the prediction neuron is linear, or a step-function; however, it could be any other nonlinearity, such as a sigmoid or ReLU 
After outputting the prediction, the neuron receives feedback in the form of the real value of the input R t   The real value is computed as R t = W c X T t + ξ, where W c = (w c 1 ,       , w c N ) is the actual value of the ingredients, and ξ is a term summarizing the noise of reward and sensing system ξ ∼ N (0, σ) 
Figure : An outline of the static agent's network  The sensor layer receives inputs representing the quantity of each ingredient of a given food at each time step  The agent computes the prediction of the food's value y t and is then given the true value R t ; it finally uses this information in the plasticity rule to update the weight matrix 
For the evolutionary adjustment of the agent's parameters, the loss of the static agent is the sum of the mean squared errors (MSE) between its prediction y t and the reward R t over the lifetime of the agent  The agent's initial weights are set to the average of the two ingredient value distributions, which is the optimal initial value for the case of symmetric switching of environments that we consider here 
As a next step, we incorporate the sensory network of static agents into embodied agents that can move around in an environment scattered with food  To this end, we merge the static agent's network with a second, non-plastic motor network that is responsible for controlling the motion of the agent in the environment 
Specifically, the original plastic network now provides the agent with information about the value of the nearest food  The embodied agent has additional sensors for the distance from the nearest food, the angle between the current velocity and the nearest food direction, its own velocity, and its own energy level (sum of consumed food values) 
These inputs are processed by two hidden layers (of 30 and 15 neurons) with tanh activation  The network's outputs are angular and linear acceleration, Fig    The embodied agents spawn in a 2D space with periodic boundary conditions along with a number of food particles that are selected such that the mean of the food value distribution is ∼ 0  An agent can eat food by approaching it sufficiently closely, and each time a food particle is eaten, it is The sensor layer receives inputs at each time step (the ingredients of the nearest food), which are processed by the plastic layer in the same way as the static sensory network, Fig   
The output of that network is given as input to the motor network, along with the distance d and angle α to the nearest food, the current velocity v, and energy E of the agent  These signals are processed through two hidden layers to the final output of motor commands as the linear and angular acceleration of the agent re-spawned with the same value somewhere randomly on the grid (following the setup of ) 
After 5000 time steps, the cumulative reward of the agent (the sum of the values of all the food it consumed) is taken as its fitness  During the evolutionary optimization, the parameters for both the motor network (connections) and plastic network (learning rule parameters) are co-evolved, and so agents must simultaneously learn to move and discriminate good/bad food 
Reward-modulated plasticity is one of the most promising explanations for biological credit assignment   In our network, the plasticity rule that updates the weights of the linear sensor network is a rewardmodulated rule which is parameterized as a linear combination of the input, the output, and the reward at each time step:
Additionally, after each plasticity step, the weights are normalized by mean subtraction, an important step for the stabilization of Hebbian-like plasticity rules   We use a genetic algorithm to optimize the learning rate η p and amplitudes of different terms θ = (θ 1 ,       , θ 8 )  The successful plasticity rule after many food presentations must converge to a weight vector that predicts the correct food values (or allows the agent to correctly decide whether to eat a food or avoid it) 
To have comparable results, we divide θ = (θ 1 ,       , θ 8 ) by We then multiply the learning rate η p with θ max to maintain the rule's evolved form unchanged, η norm p = η p • θ max   In the following, we always use normalized η p and θ, omitting norm   To evolve the plasticity rule and the moving agents' motor networks, we use a simple genetic algorithm with elitism  
The agents' parameters are initialized at random (drawn from a Gaussian distribution), then the sensory network is trained by the plasticity rule and finally, the agents are evaluated  After each generation, the bestperforming agents (top 10 % of the population size) are selected and copied into the next generation 
The remaining 90 % of the generation is repopulated with mutated copies of the best-performing agents  We mutate agents by adding independent Gaussian noise (σ = 0 1) to its parameters  To start with, we consider a static agent whose goal is to identify the value of presented food correctly  The static reward-prediction network quickly evolves the parameters of the learning rule, successfully solving the prediction task 
We first look at the evolved learning rate η p , which determines how fast (if at all) the network's weight vector is updated during the lifetime of the agents  We identify three factors that control the learning rate parameter the EA converges to: the distance between the environments, the noisiness of the reward, and the rate of environmental transition 
The first natural factor is the distance d e between the two environments, with a larger distance requiring a higher learning rate, Fig    This is an expected result since the convergence time to the "correct" weights is highly dependent on the initial conditions  If an agent is born at a point very close to optimality, which naturally happens if the environments are similar, the distance it needs to traverse on the fitness landscape is small 
Therefore it can afford to have a small learning rate, which leads to a more stable convergence and is not affected by noise  A second parameter that impacts the learning rate is the variance of the rewards  The reward an agent receives for the plasticity step contains a noise term ξ that is drawn from a zero mean Gaussian distribution with standard deviation σ 
This parameter controls the unreliability of the agent's sensory system, i e , higher σ means that the information the agent gets about the value of the foods it consumes cannot be fully trusted to reflect the actual value of the foods  As σ increases, the learning rate η p decreases, which means that the more unreliable an environment becomes, the less an agent relies on plasticity to update its weights, Fig   
Indeed for some combinations of relatively small distance d e and high reward variance σ, the EA converges to a learning rate of η p ≈ 0  This means that the agent opts to have no adaptation during its lifetime and remain at the mean of the two environments  It is an optimal solution when the expected loss due to ignoring the environmental transitions is, on average, lower than the loss the plastic network will incur by learning via the (often misleading because of the high σ) environmental cues 
A final factor that affects the learning rate the EA will converge to is the frequency of environmental change during an agent's lifetime  Since the environmental change is modeled as a simple, two-state Markov process (Fig  ), the control parameter is the transition probability p tr   When keeping everything else the same, the learning rate rapidly rises as we increase the transition probability from 0, and after reaching a peak, it begins to decline slowly, eventually reaching zero (Fig  ) 
This means that when environmental transition is very rare, agents opt for a very low learning rate, allowing a slow and stable convergence to an environment-appropriate weight vector that leads to very low losses while the agent remains in that environment  As the rate of environmental transition increases, faster learning is required to speed up convergence in order to exploit the (comparatively shorter) stays in each environment 
Finally, as the environmental transition becomes too fast, the agents opt for slower or even no learning, which keeps them ) and the decision (b ) tasks, for a variety of parameters (p tr = 0 01, d e ∈ 0, 0 1,       , 1, and σ ∈ 0, 0 1,       , 1 in all 100 combinations)  Despite the relatively small difference between the tasks, the evolved learning rules differ considerably 
For visual guidance, the lines connect θs from the same run  near the middle of the two environments, ensuring that the average loss of the two environments is minimal (Fig  )  The form of the evolved learning rule depends on the task: Decision vs  Prediction The plasticity parameters θ = (θ 1 ,       , θ 8 ) for the rewardprediction task converge on approximately the same point, regardless of the environmental parameters (Fig  ) 
In particular, θ 3 → 1, θ 5 → −1, θ i → 0 for all other i, and thus the learning rule converges to: Since by definition y t = g(W t X T t ) = W t X T t (g(x) = x in this experiment) and R t = W c X T t + ξ we get: Thus the distribution of ∆W t converges to a distribution with mean 0 and variance depending on η p and σ and W converges to W c  
So this learning rule will match the agent's weight vector with the vector of ingredient values in the environment  We examine the robustness of the learning rule the EA discovers by considering a slight modification of our task  Instead of predicting the expected food value, the agent now needs to decide whether to eat the presented food or not 
This is done by introducing a step-function nonlinearity (g(x) = 1 if x ≥ 1 and 0 otherwise)  Then the output y(t) is computed as: Instead of the MSE loss between prediction and actual value, the fitness of the agent is now defined as the sum of the food values it chose to consume (by giving y t = 1)  Besides these two changes, the setup of the experiments remains exactly the same 
The qualitative relation between η p and parameters of environment d e , σ and p tr is preserved in the changed experiment  However, the resulting learning rule is significantly different (Fig  )  The evolution converges to the following learning rule: In both cases, the rule has the form ∆W t = η p X t [α y R t + β y ] 
Thus, the ∆W t is positive or negative depending on whether the reward R t is above or below a threshold (γ = −β y /α y ) that depends on the output decision of the network (y t = 0 or 1)  Both learning rules (for the reward-prediction and decision tasks) have a clear Hebbian form (coordination of preand post-synaptic activity) and use the incoming reward signal as a threshold 
These similarities indicate some common organizing principles of reward-modulated learning rules, but their significant differences highlight the sensitivity of the optimization process to task details  We now turn to the moving embodied agents in the 2D environment  To optimize these agents, both the motor network's connections and the sensory network's plasticity parameters evolve simultaneously 
Since the motor network is initially random and the agent has to move to find food, the number of interactions an agent experiences in its lifetime can be small, slowing down the learning  However, having the larger motor network also has benefits for evolution because it allows the output of the plastic network to be read out and transformed in different ways, resulting in a broad set of solutions 
The fitness of an agent (measured as the total food consumed over its lifetime) increases over generations of the EA for both the scalar and binary readouts in the sensory network  e  The Pearson correlation coefficient of an evolved agent's weights with the ingredient value vector of the current environment (E 1 -blue, E 2 -red) 
In this example, the agent's weights are anti-correlated with its environment, which is not an issue for performance since the motor network can interpret the inverted signs of food  The agents can solve the task effectively by evolving a functional motor network and a plasticity rule that converges to interpretable weights (Fig  ) 
After ∼ 100 evolutionary steps (Fig  ), the agents can learn the ingredient value distribution using the plastic network and reliably move towards foods with positive values while avoiding the ones with negative values  We compare the dependence of the moving and the static agents on the parameters of the environment: d e and the state transition probability p tr  
At first, in order to simplify the experiment, we set the transition probability to 0, but fixed the initial weights to be the average of E 1 and E 2 , while the real state is E 2   In this experiment, the distance between states d e indicates twice the distance between the agent's initial weights and the optimal weights (the environment's ingredient values) since the agent is initialized at the mean of the two environment distributions 
Same as for the static agent, the learning rate increases with the distance d e (Fig  )  Then, we examine the effect of the environmental transition probability p tr on the evolved learning rate η p   In order for an agent to get sufficient exposure to each environment, we scale down the probability p tr from the equivalent experiment for the static agents 
We find that as the probability of transition increases, the evolved learning rate η p decreases (Fig  )  This fits with the larger trend for the static agent, although there is a clear difference when it comes to the increase for very small transition probabil-ities that were clearly identifiable in the static but not the moving agents 
This could be due to much sparser data and possibly the insufficiently long lifetime of the moving agent (the necessity of scaling makes direct comparisons difficult)  Nevertheless, overall we see that the associations observed in the static agents between environmental distance d e and transition probability p tr and the evolved learning rate η p are largely maintained in the moving agents 
Still, more data would be needed to make any conclusive assertions about the exact effect of these environmental parameters on the emerging plasticity mechanisms  A crucial difference between the static and the moving agents is the function the plasticity has to perform  While in the static agents, the plasticity has to effectively identify the exact value distribution of the environment in order to produce accurate predictions, in the embodied agents, the plasticity has to merely produce a representation of the environment that the motor network can evolve to interpret adequately enough to make decisions about which food to consume 
To illustrate the difference, we plot the Pearson correlation coefficient between an agent's weights and the ingredient values of the environment it is moving in (Fig  )  We use the correlation instead of the MSE loss (which we used for the static agents in Fig  ) because the amplitude of the vector varies a lot for different agents and meaningful The evolved parameters of moving agents' plasticity rule for the g(s) = x, identity (a ) and the step function (Eq 
4) (b ) sensory networks (the environmental parameters here are d e ∈ [0, 1], σ = 0 and p tr = 0 001)  The step function (binary output) network evolved a more structured plasticity rule (e g , θ 3 > 0 for all realizations) than the linear network  Moreover, the learned weights for the identity network (c ) have higher variance and correlate significantly less with the environment's ingredient distribution compared to the learned weights for the thresholded network (d )
conclusions cannot be drawn from the MSE loss  For many agents, the learned weights are consistently anti-correlated with the actual ingredient values (an example of such an agent is shown in Fig  )  This means that the output of the sensory network will have the opposite sign from the actual food value 
While in the static network, this would lead to very bad predictions and high loss, in the foraging task, these agents perform exactly as well as the ones where the weights and ingredients values are positively correlated, since the motor network can simply learn to move towards food for which it gets a negative instead of a positive sensory input 
This additional step of the output of the plastic network going through the motor network before producing any behavior has a strong effect on the plasticity rules that the embodied agents evolve  Specifically, if we look at the emerging rules the top performing agents have evolved (Fig  ), it becomes clear that, unlike the very well-structured rules of the static agents (Fig  ), there is now virtually no discernible pattern or structure 
The difference becomes even clearer if we look at the learned weights (at the end of a simulation) of the best-performing agents (Fig  )  While there is some correlation with the environment's ingredient value distribution, the variance is very large, and they do not seem to converge on the "correct" values in any way 
This is to some extent expected since, unlike the static agents where the network's output has to be exactly correct, driving the evolution of rules that converge to the precise environmental distribution, in the embodied networks, the bulk of the processing is done by the motor network which can evolve to interpret the scalar value of the sensory network's output in a variety of ways 
Thus, as long as the sensory network's plasticity rule co-evolves with the motor network, any plasticity rule that learns to produce consistent information about the value of encountered food can potentially be selected  To further test this assumption, we introduce a bottleneck of information propagation between the sensory and motor networks by using a step-function nonlinearity on the output of the sensory network (Eq 
4)  Similarly to the decision task of the static network, the output of the sensory network now becomes binary  This effectively reduces the flow of information from the sensory to the motor network, forcing the sensory network to consistently decide whether food should be consumed (with the caveat that the motor network can still interpret the binary sign in either of two ways, either consuming food marked with 1 or the ones marked with 0 by the sensory network) 
The agents perform equally well in this variation of the task as before (Fig  ), but now, the evolved plasticity rules seem to be more structured (Fig  )  Moreover, the variance of the learned weights in the bestperforming agents is significantly reduced (Fig  ), which indicates that the bottleneck in the sensory network is in-creasing selection pressure for rules that learn the environment's food distribution accurately 
We find that different sources of variability have a strong impact on the extent to which evolving agents will develop neuronal plasticity mechanisms for adapting to their environment  A diverse environment, a reliable sensory system, and a rate of environmental change that is neither too large nor too small are necessary conditions for an agent to be able to effectively adapt via synaptic plasticity 
Additionally, we find that minor variations of the task an agent has to solve or the parametrization of the network can give rise to significantly different plasticity rules  Our results partially extend to embodied artificial agents performing a foraging task  We show that environmental variability also pushes the development of plasticity in such agents 
Still, in contrast to the static agents, we find that the interaction of a static motor network with a plastic sensory network gives rise to a much greater variety of wellfunctioning learning rules  We propose a potential cause of this degeneracy; as the relatively complex motor network is allowed to read out and process the outputs from the plastic network, any consistent information coming out of these outputs can be potentially interpreted in a behaviorally useful way 
Reducing the information the motor network can extract from the sensory system significantly limits learning rule variability  Our findings on the effect of environmental variability concur with the findings of previous studies that have identified the constraints that environmental variability places on the evolutionary viability of learning behaviors 
We extend these findings in a mechanistic model which uses a biologically plausible learning mechanism (synaptic plasticity)  We show how a simple evolutionary algorithm can optimize the different parameters of a simple reward-modulated plasticity rule for solving simple prediction and decision tasks 
Reward-modulated plasticity has been extensively studied as a plausible mechanism for credit assignment in the brain ; ; and has found several applications in artificial intelligence and robotics tasks ;   Here, we demonstrate how such rules can be very well-tuned to take into account different environmental parameters and produce optimal behavior in simple systems 
Additionally, we demonstrate how the co-evolution of plasticity and static functional connectivity in different subnetworks fundamentally changes the evolutionary pressures on the resulting plasticity rules, allowing for greater diversity in the form of the learning rule and the resulting learned connectivity 
Several studies have demonstrated how, in biological networks, synaptic plasticity heavily interacts with and is driven by network topology   Moreover, it has been recently demonstrated that biological plasticity mechanisms are highly redundant in the sense that any observed neural connectivity or recorded activity can be achieved with a variety of distinct, unrelated learning rules  
This observed redundancy of learning rules in biological settings complements our results and suggests that the function of plasticity rules cannot be studied independently of the connectivity and topology of the networks they are acting on  The optimization of functional plasticity in neural networks is a promising research direction both as a means to understand biological learning processes and as a tool for building more autonomous artificial systems 
Our results suggest that reward-modulated plasticity is highly adaptable to different environments and can be incorporated into larger systems that solve complex tasks  This work studies a simplified toy model of neural network learning in stochastic environments  Future work could be built on this basic framework to examine more complex reward distributions and sources of environmental variability 
Moreover, a greater degree of biological realism could be added by studying more plausible network architectures (multiple plastic layers, recurrent and feedback connections) and more sophisticated plasticity rule parametrizations  Additionally, our foraging simulations were constrained by limited computational resources and were far from exhaustive 
Further experiments can investigate environments with different constraints, food distributions, multiple seasons, more complex motor control systems and interactions of those systems with different sensory networks as well as the inclusion of plasticity on the motor parts of the artificial organisms 
Context 2: Paper Info

Title: Force Feedback Control For Dexterous Robotic Hands Using Conditional Postural Synergies
Publish Date: Unkown
Author List: Dimitrios Dimou, José Santos-Victor, Plinio Moreno

Figure

Fig  1 Example of modeling the contacts and friction during manipulation 
Fig  2  Schematic representation of the proposed force controller The input is the state (GRASP or RELEASE) and the force readings Based on that the grasp size is adjusted by a value C and is given to the posture mapping function along with the desired grasp type A finger configuration is then generated and commanded to the robot 
Fig  3  Our control algorithm in Python-like pseudocode 
Fig  4  Our first experiment The robot picks up a bottle, transports it, and places down on the desk In the bottom part of the figure, you can see the control signals during this task 
Fig  5 The household objects used in our experiments 
Under the pictures of the execution you can see the signals recorded by the controller: the average normal force applied by all fingers (blue line), the thresholds f threshold high n  (purple dashed line) and f threshold low n (yellow dashed line), the average tangential force (green), and the grasp size used in each time-step (red) The task is divided four stages: 1) (red part) the initial grasp of the object, in this stage the force controller closes the grasp until the applied normal
Fig 6 In the upper row of images, you can see our second experiment The robot picks up the chips can, rotates it 90 degrees, and places back down In the middle row, for our third experiment, the robot picks up the chips can, rotates it 90 degrees, and hands it over to a person In the bottom row, for our forth experiment, the robot picks up a foam brick, rotates it 180 degrees, and hands it over to a person, using a pinch grasp 

abstract

We present a force feedback controller for a dexterous robotic hand equipped with force sensors on its fingertips  Our controller uses the conditional postural synergies framework to generate the grasp postures, i e  the finger configuration of the robot, at each time step based on forces measured on the robot's fingertips 
Using this framework we are able to control the hand during different grasp types using only one variable, the grasp size, which we define as the distance between the tip of the thumb and the index finger  Instead of controlling the finger limbs independently, our controller generates control signals for all the hand joints in a (lowdimensional) shared space (i e 
synergy space)  In addition, our approach is modular, which allows to execute various types of precision grips, by changing the synergy space according to the type of grasp  We show that our controller is able to lift objects of various weights and materials, adjust the grasp configuration during changes in the object's weight, and perform object placements and object handovers 

INTRODUCTION

To perform complex manipulation tasks in unstructured environments, humans use tactile feedback from their fingers  This feedback is provided by tactile afferents located in the skin of the hand  Particularly, for handling small objects with precise movements, the afferents located in the fingertips are used, which have high density and adapt fast to pressure changes  
These afferents provide information about the characteristics of the exerted contact forces, such as the magnitude and the direction  For anthropomorphic robots to be able to perform dexterous tasks similar force feedback signals must be used to alleviate problems arising from uncertainty in measurements, and handle external perturbations 
For example, using open-loop position control to lift a heavy object may fail due to slip without any feedback mechanism to provide tactile information  Previous works have used tactile sensors to design force controllers that use slip prediction to update the desired normal forces applied by the fingertips 
The slip predictors are based on machine learning models such as neural networks and random forests to classify multi-modal signals from a tactile sensor  In all previous works, each finger was separately controlled by an independent force controller  In addition, they required labeled data to train the slip predictors and because each finger is controlled independently is not obvious how to implement different anthropomorphic grasp types 
In this work we develop a force controller that takes as input the force readings of the fingertips and computes the grasp size which is then used along with a grasp type label to generate a grasp posture with the desired characteristics  To avoid slippage the desired normal contact force is calculated to be proportional to the tangential contact forces 
The applied normal force is then controlled using the size of the grasp as a control variable  Larger grasp sizes mean less force is applied to the object  So the grasp size is calculated from the error between the desired normal force and the actual measured normal force  The grasp size is then given to the posture sampler that generates a grasp posture, i e  the finger joint angles 
The posture sampler is modeled with a conditional Variational Auto-Encoder (cVAE) based on the framework proposed in   With this framework we abstract away the low-level control of the fingers and generate hand postures based on high-level properties such as the type and the size of the grasp  So it works as a mapping function that takes as input a low-dimensional vector and the grasp type and size as conditional variables and maps them to a set of joint angles 
We show that with our controller we can control a dexterous robotic hand to lift objects of different weights using three precision grasps  Our controller is also able to compensate and retain a stable grasp during changes in the objects' weight, for example when filling up a cup or emptying it  In addition we show how with the addition of the hand pose information we can use the controller to calculate if the tangential force is due to gravity or due to a support surface and use this information to perform handovers and place down objects on surfaces 
We perform several real-world experiments with a dexterous robotic hand to showcase the capabilities of our controller and support our design choices  To sum up our main contributions are • We develop a controller for a dexterous robotic hand that uses force feedback and the conditional synergies framework to perform dexterous manipulation tasks 
• We show that with our controller we can easily use different precision grasp types, by changing only the grasp type variable which is given to the grasp posture mapping function  • We demonstrate by incorporating information about the world pose of the hand we can use our controller to perform additional tasks such as placing down and handing over objects 
Roboticists have looked for inspiration in humans for developing methods for complex object manipulation   Neuroscientists have studied for a long time the processes that allow humans to use tactile feedback to perform complex manipulation tasks  Humans tend to adjust the grip force according to the object's weight, its friction and they use a safety margin to account for uncertainties  
To gather information about the tactile states they use multiple afferents that are located in the skin of the fingers   There are different afferents in different parts of the hand depending on their usage, e g  fast adapting afferents in the fingertips for precise manipulation  Based on signals from these afferents, humans encode simple contact events into action phases, such as grasping, lifting or releasing, which they combine in order to perform more complex and long-horizon manipulation tasks  
In robotics tactile sensors have been used for object stabilization and slip prediction in a variety of settings  For example, in , a compliant anthropomorphic prosthetic hand was controlled using force sensing to maintain object stability and avoid slip  In , they develop a control approach that uses integrated force and spatial tactile signals to avoid slip with unknown objects in real world settings 
In , , grasp quality metrics are computed based on the tactile feedback from the robots fingertips  In these works, simple two or three fingered grippers were considered for simple grasping tasks  Force control with anthropomorphic robotic hands has also been explored in more recent works  In , they employ three slip prediction methods to estimate when slip starts and based on the force signals at that moment they calculate the friction coefficient value 
Based on the calculated friction coefficient, they design a force controller that independently controls each finger to achieve a desired normal force  The desired normal contact force is set to be proportional to the tangential contact force and a safety margin based on the evidence found in   In , they train a random forest to classify the contact states into the classes: no contact, contact, slip 
Based on this classification signal, when slip is detected they increase the desired normal contact force to avoid it  In they train a recurrent neural network to estimate slip and the object material from the readings of a Biotac sensor  The force controller is increasing the desired normal contact force when slip is detected 
All these works , , use tactile feedback sensors to predict slip  They collect labeled data, on which they train their models  This approach is based on complex and expensive tactile sensors, and the process of collecting data is cumbersome  In addition, the data do not cover all possible hand poses, which would be impractical 
In contrast, in our work we do not rely on slip prediction, we avoid slip by defining a tangential force gain and a safety margin that work for a large number of objects  Furthermore, instead of independently controlling each finger we use a synergistic framework to generate grasp postures, that is conditioned on two variables: the grasp type and the grasp size 
This way, instead of controlling the values of each joint of each finger, we control only the two conditional variables greatly simplifying the control pipeline  This also, gives us the ability to use different grasp types in our manipulation tasks by changing only the grasp type variable  In also a synergistic framework was used to prevent an object from slipping from a humanoid hand, but they modeled only one synergy for a tripod grasp and they used the forces on the robotic arm as feedback, while we use force feedback from the fingertips 
Our control algorithm could also be applied to different hands as it does not depend on the hands configuration  Finally, in previous approaches only lifting tasks had been considered  In our work we demonstrate that our approach can be used to perform more complex tasks, such as placing objects on surfaces and performing handovers, which was not done in previous works 
Our goal in this work is to design a control algorithm for an anthropomorphic robotic hand to perform dexterous manipulation skills such as lifting and placing down objects  Our control algorithm will use tactile feedback from the force sensors on the fingertips of the hand to decide the forces that need to be applied to the object in each step of the task 
Given the desired forces to be applied, the size of the grasp will be computed  Given the grasp size and a desired grasp type, the posture generator will generate a grasp posture, i e  the hand configuration, such that the force constraints are satisfied  To model the contacts and friction we use Coulombs' law, which states that in order to avoid slip, the normal contact force f n to the contact surface of an object, times the fiction coefficient µ, has to be larger than the tangential force f t :
µf n ≥ f t You can see an example in Figure , where an object is pressed against a wall by an applied normal force f n , and we have the tangential force f t = mg due to gravity
Context 3: Probably one of the most frustrating things about building experimental aircraft, especially when starting with a minimum of pre-fabricated parts, is to start building and ending up with an unexpected result  Every builder starts a new project by wanting it to go "perfectly " So when things aren't going well, especially at the beginning, the frustration can lead to an unfinished airplane 
This is the first article in a series dedicated to helping builders of the Rand Robinson KR series planes build a straight and true fuselage -- the first part of the construction process  Borrowing from modern boatbuliding techniques, focus will be on the KR-2S, but the principles apply to the entire lineup of KR-1 & KR-2 series planes 
While building the KR-2(s) a common surprise is encountered by builders when the completed fuselage sides are laid into position to form the fuselage box section  With many hours spent building the sides flat, finding the once straight longerons that now bow up from the building surface, form a most dissatisfying "banana" shape  Especially when using the preformed fiberglass parts, this curve in the top longeron is not acceptable  The builder is left wondering what went wrong and no amount of clamping or brute force forming will solve the problem to any degree of satisfaction  The problem is not the builder's fault  The solution starts by understanding the three dimensional relationship of the assembled parts being built 
First understand that the plans show the finished form of the plane  They show the "projected" form as you would expect to see it if viewing an actual plane from the top, ends and from the side  Since the sides are sloped (flared) outward, looking from the side, the distances given by measuring the profile drawing are "foreshortened" and don't give the proper shape for building the fuselage with a flat top longeron  What needs to be done is to "develop" the "true" distances and shape of the flat panel so that when it is curved into position, the longerons lay flat 
Second, understand that the dimensions called for in the plans put a twist in the sides that tends to work the panel in two directions of curvature  This twist makes the panel "undevelopable" meaning that that shape cannot be unrolled into an equivalent flat shape  This is important when laying out the side and bottom panels onto flat plywood  To illustrate this, try forming a piece of paper around a soda can  The paper can be formed flat around the can either straight or at a diagonal to it's length  It has only one direction of curvature and is by definition "developable"  Now try to form the same piece of paper around a baseball  It won't lie flat on the surface without some deformation (folding, wrinkling or tearing) of the paper  The ball has curvature in more that one direction and is a "compounded" shape  Paper (or plywood) can only be readily formed in developable shapes as opposed to aluminum or other metal which can accept in plane deformation  A developable surface is needed to lay out a curved surface when the materials used can't be deformed with any degree of in-plane strain 
Initially, the fuselage sides are laid out flat with reference to the top longeron measured to a straight chalk line  The bowing problem starts when the side panels are bent and sloped to form the fuselage box section  If the sides were not sloped (tumbled home), the section formed would be cylindrical and the longerons would lie flat  Since the sides are tumbled home, the section formed is now conical  When a conical shape is cut with a plane (building surface) not perpendicular to it's axis, the shape formed is elliptical -- exactly what happens with the top longeron  When it's built flat, bent to form a cylindrical section, and sloped to form a conical section, it takes on an elliptical shape firewall to tailstock 
This method borrows heavily from proven techniques used in the marine trades  It should be stressed at this point that although the layout procedure is not complicated, it is important to take your time  If the layout is not going well initially, start over! Better to erase layout errors now than to have them built it and cause surprises later 
Layout to ensure a fair and true fuselage starts by drawing a reference line (baseline) on the building surface  Refer to figures 2 & 3 and use a wire guide to draw a very straight baseline  About 500 lbs  Of tension should be adequate  One could use a chalk line, but we're talking airplanes here, not house framing 
The main layout difference is that the baseline isn't used as a reference for the top longeron  The baseline references the mid point of the firewall for the developed (and true dimensioned) side panel  Although the baseline will still be the reference, the top and bottom longerons will be laid separately 
Layout differences don't end there  Each of the stations (vertical members) will be laid out with a calculated separation so that when the panels are formed into position, they land on the spacing called for in the plans  Another major difference is that the bottom & side panels are applied after forming the fuselage box section  This is mainly to obtain the ability to "fair" the side and bottom surfaces and insure a straight and true shape 
Refer to figure 1 for the layout of the new developed side panel  The firewall (station a) is layed out perpendicular to the baseline  Longitudinal (station) measurements are given along the length of the baseline from the firewall  Vertical dimensions are given to reference the angle and breadths of the station at the baseline 
Notice that the top longeron is bowed outward and that the stations are spaced slightly greater than called out in the plans  When the panels are formed into the box frame section ,they will work into the dimensions specified in the plans 
Strike a centerline, longer than is needed on the building surface using a wire guide  Draw off the firewall line perpendicular to the centerline at one end 
Using the distances listed in the balloons, mark them off on the centerline  Distances are measured to the nearest sixteenth of an inch  Take time to mark them off carefully  Don't mark off the distances in a cumulative fashion  Use the firewall as a common reference 
Using the angles listed at each station, mark off a station line longer than is needed  The angles are measured to the nearest hundredth of a degree  Take time to mark them off carefully 
At each station, start by marking off each short (bottom longeron) line distance from the centerline  Use your set of trammels or beam compass for doing this  Mark the intersection of the short line with the station line 
At each station, mark off each long (top longeron) line distance from the intersection of the short line distance and the station line  Again the trammels or beam compass is best for completing this step  Mark the intersection of the long line distance with the station line 
Using the longeron as a batten, trace out the inside and outside curves of the longeron  After the batten is secure, in between each station, fasten a keeper block inside and outside to preserve the shape of the longeron taking care to avoid potential future interference with the diagonal members to be installed later  The fairing blocks can be removed or left in place if they won't interfere with building  The vertical station members and their diagonals can now be measured and positioned  Remember to refer to the plans for the material thickness direction 
After vertical and diagonal members are cut and fitted, take time to draw their outlines on the building surface to cut down on time and confusion when laying out the opposite side 
Finishing the side panel is accomplished in a manner similar to that called for in the handbook with the exception that the side and bottom skin panels will be attached later 
The next article in the series will discuss jigging and building techniques to ensure alignment and straightness of the flat built side panels  Also covered will be building a "strongback" jig to assure alignment of the side panels when they are formed into their final shape 
Part 3 in the series will cover assembly of the side panels using the jigs  Some joint details will be discussed that will ensure a stronger and more fair fuselage assembly  Also covered will be the layout & attachment of the side and bottom ply skins 
U S  Mail: Densmore Associates, inc 
ANSI "D" size, computer generated plots of all the layout drawings in this series are available from the author for $30 plus postage & handling  Full (true size) scale plots may be made available depending on demand 
"Scarfing" is the practice of splicing plywood so that short pieces of plywood can be used to span long distances  On the KR, it is required on both the fuselage skins and spar webs  The angle of the splice should be 10 to 12 degrees to maintain strength across the joint  Also, joints should coincide with structural members, such as spar webs or fuselage truss members 
This scarfer is made by mating a regular plunge router (this one costs about $50) to a table saw  Obviously, you really only need a table saw to cut the chamfer, but it does make a nice heavy table for scarfing  You could just as easily use a large work table as the base First, set the table saw for a 5 5 degree cut (for a 1:12 joint, or 6 5 degree cut for a 10:1 joint), and run a 1 x 6 through on edge to chamfer a corner on the board  Then drill the board for three router mounting holes (two are countersunk) and connect the assembly to the table saw with two 1/4 inch bolts  Use a long (2-3 inch) straight cutting bit to do the cutting  Adjust the bit so it doesn't interfere with your table top, and go to town  Keep pressure on the plywood to ensure contact with the table while you're scarfing  Make sure you feed your material from the same end as you would if you were sawing, or the router will take your plywood away from you and put a big dent in your garage door 
In the late 60's Ken Rand and Stuart Robinson were working as flight system engineers for Douglas Avionics  Ken was working as an electrical engineer, having previously worked for Sperry as an autopilots project engineer, while Stu's degree was in aeronautical engineering from Northrop University  They were two of the guys at the end of the DC-8,9, and 10 assembly lines responsible for correcting some of the nits and picks in various systems before delivery to the customer 
They both wanted to build a fast, inexpensive airplane which was also economical to maintain  Several designs were considered, and plans were bought first for the Jeanie's Teenie and then the Taylor Monoplane  The Monoplane was more to their liking, but would require some modification to fit their needs  A cooperative redesign effort ensued, with virtually no dimensions left untouched  Only the basic fuselage structure, airfoil, and powerplant were retained  The tail shape was Stu's, and came directly from the big DC-8s parked on the ramp outside his office window  The landing gear was designed by Ken, after seeing the gear on a Dewey Bird at Santa Paula airport 
Ken was killed in his KR2 a short time later while flying over Cajon Pass in what was apparently a bad weather / low fuel accident  Ken's wife Jeanette became owner of RR overnight, and stepped up to keep the plans and parts coming  Much of the engineering needs are handled by Bill Marcy of Denver, who's been helping out since early '79 
To date, almost 6000 KR1, 9200 KR2, and 760 KR2S plan sets have been sold  1200 KR2s are estimated to be flying, with 5 KR2Ss now in the air  Much of the development work done on KR's is now done by the builders themselves  KR builders tend to be innovative, which leads to some interesting modifications  Some of the mods that work eventually creep into the plans  The KR2S is a case in point  Many builders who'd heard of the pitch sensitivity and tight cabin of the KR2 began to build an enlarged version, with the length determined by the most commonly available longeron material  The result is a KR2 that is stretched 2" between firewall and main spar, and 14" behind the main spar  Higher gross weights dictated more wing area, with the new standard becoming the Diehl wing skin  Those who plan to carry passengers commonly stretch the cabin width a few inches, although 1 5 inches is the limit if you still want to use RR's premolded parts 
Mike Stearns addresses the KR Forum crowd 
This year's KR Forum featured guest speakers Mike Stearns, Steve Trentman, and Bill Marcey  Mike Stearns spoke on several topics, including the many sources for KR and homebuilding information available on the Internet  He also mentioned KRNet, the list server devoted entirely to KR aircraft, as well as several notable World Wide Web home pages  He also brought a sample of the new Rand Robinson wing skins with him, and discussed their high temperature core prepreg construction  His KR2S will receive the first set, which is currently being installed at Hinson Composites 
Steve Trentman spoke on his turbine installation  It uses a turbine engine which saw duty as an A7 attack jet starter engine  Total weight is about 85 pounds, while putting out around 90 horsepower  There is a small stockpile of these engines available from government surplus  sources  This engine can only be throttled back to 52% power, which leads to some pretty interesting landings  One inflight failure has been logged so far, with very little damage to the aircraft  More on this exciting development in next month's issue of KROnline 
Les Palmer's KR2 N202LP won Best KR2, Best Engine Installation, and People's Choice awards at the 1995 KR Gathering at Columbia, TN  After researching the KR series, and reading Neil Bingham's "A Critical Analysis of the KR2" (Jan 88 Sport Aviation), Les decided to build his as a single seater, stretched 24" in the tail, while maintaining a stock width firewall  His fuselage is made from Douglas fir, which weighs in at 4 lbs heavier than if constructed from spruce  It is skinned with 1/8" birch plywood  Spars are covered with plywoood on both fore and aft sides, ala KR2S  Diehl wing skins provide the lift  Horizontal stabilizer and elevator were stretched 7" longer on each side, while the vertical stabilizer and rudder were stretched 8" taller    The fuselage to cowling junction was made more graceful by adding 1 5 inches to the height of the firewall end of the fuselage sides 
Les's canopy is a Dragonfly, using a four linkage system to swing forward when opening  The canopy frame fits snugly into a recess in the foward deck, providing an excellent wind and water seal  The fiberglass work is exemplary 
Seating is luxurious for one 
The cowling is also a work of art, and uses NACA ducts for efficiency  Female molds were made for all the fiberglass parts on Les's plane, so he could proabably be persuaded to make more, if demand dictates  Les also machines a multitude of KR aluminum and steel parts which he now offers for sale 
The firewall was reinforced with aluminum brackets and angles bolted between the longerons in anticipation of the 200 lb Subaru EA-81 engine installation  His 100 HP Asian version is outfitted with an American Holley 5200 caburetor and manifold  It uses a PSRU of Les's own design, featuring two spur gears with a 1 69:1 reduction ratio and a toothed belt  Other than tapping the crank for larger bolts to mount the redrive, no other engine modifications were required  Also, this is probably the only air conditioned KR2 on the planet  The prop is a 60/63 Hegy



ground_truth: Environmental fluctuation and uncertainty control the reliance of artificial organisms on plasticity.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How many experiments were demonstrated to test the capabilities of the controller?

Read the following text and answer briefly.

Context 2:  In order for the object to remain stable we need to apply a normal force: where µ is the friction coefficient between the object and the wall 
In the case of a dexterous hand manipulating an object, we want the normal forces applied by all fingers to be greater than the tangential force divided by the friction coefficient of the materials of the object and the fingertip  Since it is hard to accurately compute the friction coefficient between all possible object materials previous works have used multi-modal tactile sensors like the BioTac sensor, which provides information about the pressure, skin deformation, and temperature, to predict slip and based on that signal to increase the applied normal force 
In our work we use the FTS3 sensors which is a low-cost sensor that measures the 3D force applied in each fingertip  In addition, previous works gathered labeled datasets in order to train their slip prediction models which is time-consuming and limits the possible orientations of the hand, because gathering labeled data for all possible orientations is impractical 
To overcome this we experimentally selected the parameters that determine the value of the applied normal force such that we avoid slip for all objects in our dataset, from the lightest to the heaviest  In order to guarantee contact between the fingertip and the object, in the beginning of the grasping phase, we use an offset f of f set n as the minimum normal force applied by each finger 
In they also suggest that humans use an additional safety margin which is proportional to the tangential force, f margin n ∝ f t   So the final desired normal contact force becomes: where G is the gain that includes the friction coefficient and the additional safety margin  To alleviate the effects of noise in the sensors, the running average of the measured normal force f n and tangential force f t is used, as a low pass filter 
So for each force measurement we have the following relation: where α ∈ (0, 1) is a parameter that determines how much new measurements affect the value, and is experimentally selected  Given the measured normal force f n from the fingertip sensors we can compute the error f err n = f des n − f n   We use this error signal to control the grasp size variable g size , that we use as a conditional variable in our posture mapping function 
The grasp size represents the distance between the thumb and the index finger in a grasp posture  So a smaller grasp size will result in a tighter grasp and greater normal force applied to the surface of the object  We use a linear controller for the grasp size variable that is implemented as follows: where K is a parameter that controls the rate of decrease of the grasp size, and is experimentally selected 
So when the error between the desired normal force and the actual normal force is large the grasp size decreases so tighter grasp postures are generated in order to apply more normal force  In practice, in order to avoid oscillations in the grasp size we use the desired normal force as a high threshold that we want the measured normal force to be below:
If the normal force is below that threshold the grasp size does not change even if there are small oscillations in the measured tangential and normal forces  Also, in order to avoid the hand applying too much force that damages the hardware or the object we use a low threshold, that is: where w threshold is the width of the threshold in mN  
If the measured normal force is below the grasp size increases in order to apply less force  So the final grasp size variable for grasping is calculated as follows: where This is similar to the deadband control method , where instead of having a fixed reference point, an operating range is set  If the response is in this range, the controller does not exert any correction 
In our case, the operating range changes according to the force signals from the robot's fingertips  The grasp posture mapping function is based on the conditional postural synergies model presented in   It uses a conditional Variational Auto-Encoder model to generate grasps postures conditioned on additional variables such as the grasp size 
In this work we augment this model to also generate grasp postures conditioned on the grasp type  The model is trained on a set of labeled grasp samples acquired by teleoperating a robotic hand using a data-glove  Using this model we are able to abstract away the low-level control of each joint of each finger and generate grasps based on more general characteristics such as the type and the size of the grasp 
In this way we can control all the fingers jointly by a single value, the grasp size, thus greatly reducing the control parameters  In addition we are able to use the same control algorithm for different precision grasp types, by changing the grasp type conditional variable  Finally, we can modify our controller to release objects instead of grasping them 
Given the pose of the hand in the world coordinate frame, which we can acquire from the robotic arm that is attached to, we can use the forward kinematics of the hand to compute the poses of each fingertip  Then using the force readings of each fingertip we can calculate the global direction of the net tangential force 
If the angle between the direction of the net tangential force and the direction of gravity is less than 90 degrees, i e  the net tangential force's direction is towards the ground, we assume that the tangential force is due to gravity pulling the object, so the force controller tries to grasp it  If the angle is more than 90 degrees, i e  the net tangential force's direction is upward, it means that something is pushing (or pulling) the object upward, in which case we assume that the object is touching on a support surface or someone is pulling the object so the controller increases the grasp size given to the posture mapping function proportionally to the normal force measured thus slowly releasing the object 
Opening the grasp is done by controlling the grasp size variable as follows: That way we can place objects on surfaces but also perform robot to human handovers, where the robot holds the object and the human grasps the object and slightly pushes or pulls it up, signaling to the robot that there is a support surface 
The robot then slowly releases the object by opening its grasp  We showcase these scenarios in the experiments' section  Based on these observations, we present our force controller in Figure   The hand starts in an open pre-grasp position, a latent point is sampled from the prior distribution of the posture mapping function, and given the desired grasp type and the grasp size a grasp posture, i e  the joint angles of the fingers, is sampled 
The initial grasp size is set to the maximum value, and when the force controller comes into effect and depending on the state of the system and the forces on the fingertips grasp size changes by some value C, according to equations 1,2, until the desired normal force is achieved  To choose between grasping or releasing an object we use a finite state machine formulation 
When the hand reaches the desired grasp pose, which we assume is provided, the GRASP state is activated, in which the controller tries to grasp the object  When the controller detects that the tangential force applied to the object is coming from a support surface the state changes to the RELEASE state, in which the controller releases the object by opening the grasp 
You can see the full algorithm in Python-like pseudocode in Figure   To summarize, the advantages of our controller compared with previous approaches are threefold: 1) instead of controlling each joint of each finger of the hand we use only two variables, the grasp size and the grasp type, which allows us to perform multiple grasp types by changing only one variable while the grasp size variable is common among all grasp types, that greatly reduces the complexity of the control process compared to independently controlling a 21 DoF hand to perform different grasp types, 2) we do not rely on slip prediction for controlling the desired normal force, which involves gathering labeled data and works only for the hand poses in the training dataset, and 3) we can use our controller to also release objects instead of only grasping them 

Experimental Set-up 

For our experiments we used the Seed Robotics RH8D Hand , which is a robotic hand with 7 DoFs  The hand is equipped with the FTS-3 force sensors in each fingertip, which are high resolution tactile sensors that provide the 3D force applied in each fingertip  The sensor provides data at a rate of 50Hz  For the experiments the hand was mounted on a Kinova Gen3 7DoF robot 
To train the posture mapping function we used the CyberGlove to teleoperate the hand and collect 468 grasps belonging to three precision grasp  types: tripod, pinch, lateral tripod  The architecture of the cVAE model was the same as in , with the addition of the grasp type as a conditional variable, which was one-hot encoded 
We used 10 household objects shown in Figure   With the heaviest object weighing 380g and the lightest 1g  During the experiments the trajectories of the arm were prerecorded, while the hand was controlled online by our control algorithm 

Parameter tuning 

To select the values of the parameters in our controllers we conducted preliminary experiments where we tested lifting and releasing several objects, with different physical properties  To select the value of the normal offset force f of f set n , we used an empty plastic cup as our test object, and we choose a value such that the fingers do not deform the cup 
The final value of the parameter was set to -50 mN  To select the values of the gain G and the rate of decrease K, of the grasp size, we experimented with the heaviest object in our dataset, which is the mustard bottle and weighs 380g  The gain G was set to 2 0 such that the desired normal force would be enough to hold the object 
The rate of change of the grasp size was set to 100 0, based on the operating frequency of the force sensor and the range of values of the tangential force  For the tangential force averaging process we used a parameter value of α t = 0 7, because we want the controller to be sensitive to fast changes in its value, that can arise for example during lifting an object 
For the normal force averaging process we used a parameter value of α n = 0 5, as we do not want it to be affected by noise that could make the controller overconfident 

Experiments 

To explore the capabilities of our controller, we demonstrate five experiments of increasing complexity: 1) we picked and placed a bottle using a tripod grasp, 2) we picked, rotated and placed a chips can on a box using a tripod grasp, 3) we picked, rotated and handed over the chips can to a person using a tripod grasp, 4) we picked, rotated and handed over a brown foam brick to a person using a pinch grasp, 5) a person handed over a plastic cup to the robot, filled it with coins to increase its weight, and the robot then handed it back to the person using a tripod grasp 
You can see the execution of the first experiment in  In the middle row, for our third experiment, the robot picks up the chips can, rotates it 90 degrees, and hands it over to a person  In the bottom row, for our forth experiment, the robot picks up a foam brick, rotates it 180 degrees, and hands it over to a person, using a pinch grasp 
Fig    In our fifth experiment, a person hands over an empty plastic cup to the robot, throws coins in it to increase its weight while the robot adjusts its grip to stabilize the object, and then hand overs the cup back to the person  force is below the offset f of f set n , 2) (green part) the robot lifts the object, as it tries to lift the tangential force increases, increasing the threshold, so the grasp size decreases to apply more normal force, 3) (orange part) the robot transports the object, you can see, in point A in the Figure, a perturbation in the tangential force when the robot begins to move, the controller responds by decreasing the grasp thus stabilizing the object, and 4) (blue part) the robot enters the releasing phase, where it lowers the arm until it detects that the tangential force is due to a support surface, then it stops lowering the arm and increases the grasp size slowly releasing the object 
In point B in the Figure, you can see that there is noise in the tangential force, due to the arm moving to place the object on the table, that is also reflected in the desired normal force  Because we use the desired normal force as a threshold and not as a reference signal this noise is not manifested in the control of the grasp size 
You can see the execution of the second experiment in the upper part of Figure   This experiment demonstrates the ability of the controller to handle arbitrary hand poses  The experiment is divided in four parts: 1) the robot enters the GRASP phase and the force controller generates grasps to achieve a normal contact force below the f of f set n threshold, 2) the robot lifts the object and adjusts the grasp size to avoid the object falling, 3) the hand rotates to place the chips can on the horizontal position, and 4) the robot enters the RELEASE phase, and the arm lowers until the object touches the box, when the hand detects the supporting surface, it starts to slowly release the object 
You can see the execution of the third experiment in the middle part of Figure   This experiment demonstrates the ability of the controller to perform robot to human handovers  The experiment is divided in four parts: 1) the robot enters the GRASP phase and the force controller generates grasps to achieve a normal contact force below the f of f set n threshold, 2) the robot lifts the object and adjusts the grasp size to avoid the object falling, 3) the hand rotates to place the chips can on the vertical position, and 4) the robot enters the RELEASE phase, the arm stays still, the human grasps the object from the bottom and slightly pushes it up, the hand then detects that there is a supporting surface and starts to slowly release the object 
You can see the execution of the fourth experiment in the bottom part of Figure   This experiment is similar to previous one, but the grasp type that the robot uses is a pinch grasp, that involves only the thumb and the index finger  To perform this we only had to alter the grasp type conditional variable that was given to the posture mapping function 
You can see the execution of the fifth experiment in the bottom part of Figure   In the first part (blue) of the experiment the robot closes its grasp, by reducing the grasp size, until the normal force is below the force offset  In the next three parts (pink, green, red) the person throws coins in the cup to increase its weight 
You can see in the signal plots that each time coins are added the tangential force decreases so the normal force threshold decreases too  The grasp sizes then decreases as well in order to apply more normal force  This experiment demonstrates the ability of the controller to handle perturbations in the weight of the object during grasping 

CONCLUSION

In summary, we presented a controller that uses force feedback integrated with conditional synergies to control a dexterous robotic hand to grasp and release objects  We demonstrated that our controller can lift objects of different weights and materials while avoiding slip, react online when the weight of the object changes, place them down on surfaces, and hand them over to humans 
In addition, the control architecture is modular, so the synergy grasp mapping component can be easily changed in order to control several precision grasp types  However, our experiments also revealed various limitations of our controller  For example our method fails to stabilize the object when rotational slip occurs 
In addition hardware limitations such as, slow update rates and noise in the force measurements can create problems that result in the object falling  In future work we plan to incorporate additional sensing modalities, such as vision to alleviate some of these issues 



ground_truth: 5.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the problem encountered when building the fuselage sides?

Read the following text and answer briefly.

Context 3: 
Originally built as a taildragger, the fixed gear is made from 4130 steel tubing  Custom cast 6 00x6 aluminum wheels and steel rotors are mated with 6" Cleveland calipers for braking  An early taxi test accident damaged the main gear, and prompted Les to change to tricycle gear  Again, he designed his own fiberglass main gear, and uses a Diehl nose wheel fork with a 4130 strut and 6" wheel up front 
Early tests revealed cooling problems, which prompted a radiator move from the firewall to a lower cowling location 
The first flight was almost a disaster, as test pilot Randy Smith lost power right after takeoff  He managed a 180 with a safe downwind landing with only minor nosewheel pant damage  The culprit proved to be a spark plug with too much reach, which was quickly remedied  Subsequent flights have shown water temp to be about 210 degrees, oil temp is 220-230, and airspeed is about 180 mph 
Shopping for the Partially Built KR 
This story starts about twenty years ago when I first started looking at the KR-2 as the plane I'd like to build  The only problem at that time was a lack of money, lack of knowledge, and a lack of job stability  I liked the design, except for the low ground clearance of the retractable gear and that a KR was going to be a tight fit for me to fly 
Over the past twenty years I've owned a number of planes, but still always wanted to build my own  I needed one that would fit me, my budget requirements, and have the speed and performance that I wanted  When "KITPLANES" published the article featuring Roy Marsh's new KR-2S, it was the first I had heard of any major modifications or improvements to the same old KR design  I believe that article and Roy Marsh's workmanship have probably been the greatest boon to Rand Robinson (RR) in the last twenty years  It certainly caught my eye! Here was the same design I had decided I wanted to build twenty years ago, with all of the improvements I wanted  It was sitting on fixed gear with some reasonable ground clearance  It had the capability to be built large enough to accommodate me  It has enough prefab parts available that it didn't have to be 100% scratch built if I decided to hurry the project along  And it had the speed I wanted  I knew that Roy's published speeds were probably not realistic expectations for the average KR, but after knocking around for the last three years in my Champ, anything over 90 mph seems pretty fast to me 
After purchasing the info kit and the sales video from Rand Robinson, the next step after deciding for sure to build this plane was to order the KR-2 plans and the KR-2S addendum  I finally got my plans and was putting together my first order to start the plane, when my partner in the Champ pointed out that there was a partially completed KR-2S for sale in Trade-a-plane  My initial answer was "No, I don't even want to look at it  I want to build my own from scratch " My partner insisted that for the advertised price and the fact that it wasn't too far away, I ought to at least give the guy a call and investigate it  "No, I don't think I want to buy someone else's problems," I persisted  That night I went home and crunched up some numbers on the calculator and finally came to the conclusion that for the sake of my budget for the next several years, I really should give this guy a call 
Three days later, I flew to his place about 400 miles away to take a look at his project  At this point I should probably mention that I consider myself to be fairly knowledgeable about airplane construction, although the vast majority of my experience is with tube and fabric  The rest of this article deals with what I looked for and more importantly what I missed and have had to repair in the last year since I purchased the project 
When we went to the seller's house, I found that the left wing was built using the Dan Diehl wing skins and the right wing skins were leaning against the wall inside the house  Also the canopy was in the house with the canopy covered with paper and tape  I wanted to inspect the fuselage first, so off we went to the shop 
There I found a fuselage sitting on it's gear painted in primer gray  The first step was to inspect the quality of workmanship of what could be seen as it sat  The interior of the fuselage looked as if it had been built with a great deal of care  The fit and finish of all of the interior wood was very nice  Even the gussets looked like they had been painstakingly perfectly fitted  The glass work on the turtle back also looked very precise and clean  It was evenly faired into the vertical and horizontal stabs  The tail also appeared to be well built with the exception of a depression directly over the front and rear spars in the horizontal stabs  He explained that when he moved recently, that he had shot the plane with gray primer to protect it from the weather since he wouldn't have ready access to a shop to put it in right away  It ended up sitting out in the hot south Texas summer sun for a few weeks before he got a shop rented to work in  That caused the glass (or possibly the foam inside the horizontal stab) to swell, except that it held onto the spar, so it was slightly ballooned in front of and behind the spars  His recommendation was to fill it back smooth with micro 
I also found a small linear crack in the lower left wing spar cap on the left wing stub  It appeared to be from over tightening the rear spar wing attach fitting bolts  His explanation was that the crack wasn't important because the rear spars only job is to keep the wings from folding back  I also noticed that the holes for attaching the outer wing to the wing stub were badly rounded out on the rear spar  He explained that the Diehl wing skins require the rear spar to be swept slightly more forward than the stock wings  This won't allow you to use the rear spar attach fittings from RR and that I would need to fabricate a new set of rear spar attach fittings 
I also found that the aileron bellcranks were not built or installed as per plans, but found that they looked professional  I couldn't check for function since the right bellcrank and sheeve wasn't installed, the left wing also wasn't installed, and the right wing didn't exist yet 
Next we pulled the inspection panels off of the fuselage and tail and looked at everything I could see with a good flashlight  I didn't find anything else that might be questionable about the fuselage except for a cracked elevator trim tab that was damaged when it fell off it's hanging place on the wall 
Next we spent some time going over his builders log and builders photo album  I still hadn't seen anything that would dissuade me from buying this project 
At this point it was starting to get late and my ride down needed to get airborne for the flight home  I needed to make a decision about whether I wanted this project or not, but I hadn't inspected the wings and canopy yet  I took a cursory look at the left wing and saw lots on micro built up on it and some bubbles in the leading edge, but nothing that looked seriously wrong to my amateur eye  The right wing was only a set of spars in the shop and the Diehl wing skins in the house, so there wasn't much to look at there  The canopy was wrapped in paper and tape, so there wasn't much to look at there either  I decided that even if there were serious problems in the wing that was built, I would be money ahead to go ahead and buy the project  For the advertised price, I could build a new set of wings and still be way ahead financially  We negotiated a final price, shook hands, took my ride to the airport, and started off in search of a U-haul to haul the project home 
Now, at this point, some of you are thinking about what I surely must have forgotten to inspect and why didn't I take a local A & P or EAA member along for the ride  First of all, I don't know any mechanics locally that have any experience with glass and our EAA chapter of which I am VP is woefully lacking in fiberglass knowledge  Secondly, as you will see, I missed plenty  Some by ignorance, some by just not looking close enough 
Now for a list of the problems that I found over the last year and a few of the fixes that I came up with 
I found that the lower set of rear spar attach fittings on the left rear spar were installed backwards with the longer spaced hole towards the fuselage  Since this is the same place that also had the cracked spar cap, it required a major change  Also in the same area he had drilled through the rear spar with a hole saw to create a place for the aileron cable to pass through and managed to cut out the second from the outside vertical brace in the spar  Then he chose to install the aileron bellcranks in front of the rear spar, and cut another hole through the rear spar for the aileron push rod  He also managed to cut out the outside vertical brace in the spar  Since the holes were already drilled through the spar, the choices were to either cut out that section of spar cap and scarf a new piece in, cut the whole rear spar carrythrough out of the fuselage including ruining the left lower wing skin, or do something else creative to reinforce the spar cap and install a custom built set of attach fittings 
I also found that after I built and installed the right side wing stub ribs and skin that the aileron bellcrank setup would not work as installed  The cable that crosses between the two bellcranks had a sharp uphill from the sheeve to the bellcrank in the last 12 inches on either side  This combined with the radius that the bellcranks turn caused the cross cable to pull up tight when the ailerons were pushed to either end of their travel, but allowed the cables to go very slack when the ailerons were centered  Also the Aileron pushrods needed to pass directly through the lower set of rear wing attach fittings to attach to the aileron  This whole rear spar and aileron bellcrank setup was going to either have to be redesigned or cut out and built to plans  The bottom line is that the problems I observed when I inspected this part were much more serious than expected when I had to fix it 
I decided that I had to remove the rear fittings from the left wing to be replaced with the new set that my neighborhood machinist was cutting out for me  When I put the wing on the work bench to start removing the rear fittings, I thought I had better take a closer look at the bubbles in the leading edge  I found that as I pushed on the leading edge, it delaminated between the glass lay-up on top and the upper and lower wing skin edges that were floxed together underneath  I concluded that that area had to come apart and took a belt sander to the leading edge  What I found was that the leading edge had been floxed together and glassed over, but the mold release had never been scrubbed off the leading edge of the wing  It peeled apart for rebuild quite easily 
When I got back to removing the rear spar attach fittings, I noticed that the woodwork inside the wing looked awfully dull  The reason was that the wing had been closed up without varnishing any of the woodwork  This was rectified with a small hole saw, a number of extensions and a modified undercoating sprayer 
I also found that the aluminum drain fitting in the bottom of the left wing tank had been glassed into place upside down  The tapered pipe threads were tapered the wrong way to install the draincock into the tank  Retapping the fitting the right direction seemed to be a good fix for that problem 
When I finally got around to attaching the wing to the fuselage, I found that the front spar attach fittings were badly misaligned  Although they could be forced into alignment, I didn't think I needed that kind of preload on the main spar fittings  This problem was fixed by calling on my local neighborhood machinist to build me an aligning fixture and reaming the attach holes to the next larger size and ordering the new sized bolts 
On the fuselage I found that although it had new Cleveland wheels and brakes on it, one of the brakes had a severe wobble to it  I must complement the manufacturers for taking care of that problem  One call to the Cleveland factory and they shipped me a new set of wheels and brakes even though the receipt for this set was over four years old and in the original builders name  Their only concern was that this set had never been placed in service yet 
I chose to sand the load of micro off the left wing to see what it was covering  When I got down to the glass, I found that there was no glass for the aft inch and a half of the underside of the wing in front of the aileron hinge  With the Diehl wing skins, you build the wings, then cut the ailerons out of trailing edge of the wing  He had mismeasured and cut too much material off the bottom side of the trailing edge in front of the aileron  It was filled by floxing a piece of spruce into the gap to fill the space between the back edge of the fiberglass and the aileron mount  I chose to wrap the trailing edge of that wing, and the other wing to match with a couple of lay-ups of glass 
When I sanded the primer off the aforementioned damaged trim tab, I found that the hinge was floxed to the leading edge of the foam insides of the tab, but not the glass  I also chose to wrap the front of the trim tab with a lay-up of glass 
I decided to pull the paper off the canopy and take a look at it before I'm ready to bolt it on and fly  The original builder had blown his own canopy and after some of the previous problems, I was beginning to have some concerns about not having looked it over closely enough  The canopy turned out to have been blow a little too large  It ended up with a little larger bubble for headroom, which I didn't object to  However, it had more headroom on the right side than the left  Yes, it was just a little bit lopsided  The main problem was that the canopy is stretched thin enough that it can be easily pushed in with one hand when the weather is warm   My fear was that this is just thin enough that it may decide to lay on my head or in my lap when flying on a warm day  It will have to be replaced 
I'm sure that many that are reading this could see several of the potential problems before I mentioned them, but some others may not have and I'm sure that there could have been many other problems that didn't but could have existed on this project  This is also not intended to be critical of the gentleman that started this project as many parts of it, especially the wood work are better than I could have done and much of his work is outstanding  I prefer to think that I'll end up with a better plane with his woodwork combined with my glasswork  This article is intended to feature some of the problems that you may run into in buying someone else's project 
The final question is, knowing what I have found over the past year, would I have still purchased this project  The answer is yes, but primarily because the price was right in that I am still money and work ahead of where I would be if I had started the project from scratch  There are a few things that I would have done differently, but nothing that I can't live with  Although I won't be able to say that I built it all from scratch, I have built and rebuild enough of the plane that I should have no problem qualifying under the 51% rule 
You can send comments directly to the author via e-mail at "jscott@LANL GOV" 
Here is an brief explanation of how I built my turtledecks  The jig was constructed from scrap plywood and a few 1x4s that I ripped into stringers  I made two temporary bulkheads from the plywood, one for each end  Remember the forward bulkhead needs to be shaped in a way that will closely match the aft end of your canopy frame  Make an aft bulkhead by placing a straight edge at the top of your forward bulkhead and the trailing edge of your horizontal stabilizer  This will give you an idea of how tall your aft bulkhead needs to be  As far as location, I placed my aft bulkhead just forward of the lower/front of my vertical fin  I constructed the jig on the fuselage, it is glued together with automotive bondo 
After the bulkheads were bondoed to the fuselage I used the stringers that I ripped from the 1x4s and bondoed them to the bulkheads  This gave me a male form to cover with thin plastic or posterboard  I stapled two layers of posterboard to the jig(thin plastic would work better)  The posterboard wraps down two inches onto the fuselage  After I was satisfied with the way it looked, I then covered the entire thing with duct tape (fiberglass will not stick to duct tape) On top of this I wetout one layer of tri-ply cloth (22oz) that I had left over from an earlier project, and one layer of 8oz  bid  Remember to mask off your fuselage so you don't get epoxy on it  If you are not familiar with composite lay-ups, you should plan on razor cutting your lay-ups 4 to 6 hours after wetout while the lay-up is still soft enough to cut with a razorblade 
After the lay-up cured (2 or 3 days) it was removed from the jig, and the jig was removed from the fuselage and discarded  (be careful, the bondo sticks very well to the spruce, you could splinter your wood during removal) I now have a fiberglass skin that tends to hold the shape of the jig but is still flexible enough to work with  I made two bulkheads out of 1/4 last-a-foam (AS&S) using the plywood formers from the jig as a guide  I covered these foam bulkheads with one 8oz layer of glass on each side, with a glass to glass edge on the bottom  After cure these bulkheads were bondoed into place (to the fuselage)and the fiberglass skin was pulled down tight and floxed to the bulkheads  When the flox cured the bondo joints were broken, again being careful not to harm the wood  The turtledeck was removed from the fuselage and 2 inch tapes added to the bulkheads inside and out 
At this point the turtledeck looked great and only weighed about 5lbs  but I noticed you could deform the skin by pushing hard on the outside  So I flipped the turtledeck over and from 1/4 inch last-a-foam, I cut two inch wide strips that would run the entire length, forward and aft inside the turtledeck  In effect these would act as composite stringers, I made enough of these two inch wide strips to make up three stringers  One down the center (sort of a backbone) and one on each side of the "backbone" half the distance to the edge of the turtledeck  I sanded the edge of the foam so that when covered with a layer of bid @ 45degrees there would be a nice transition from the turtledeck skin up onto the foam and then back onto the turtledeck I scuff sanded and glued the foam stringers in with micro  I covered the foam stringers with one layer of 8oz bid @ 45degrees 



ground_truth: The longerons bow up from the building surface, forming a "banana" shape.