Read the following text and answer briefly.

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. 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.

Now, answer the following question based on the above text, 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?
Answer:



Answer: 5.