Inverse dynamics control and feedforward linearization techniques are typically used to convert the complex nonlinear dynamics of robots to a set of decoupled double integrators, and then a standard, outer-loop controller can be used to calculate the commanded acceleration for the linearized system. However, these methods typically depend on having a very accurate system model, which is not available in practice. While this challenge has been addressed in the literature using different learning approaches, most of these approaches do not provide safety guarantees in terms of stability of the learning-based control system. In this paper, we provide a novel, learning-based control approach based on Gaussian processes (GPs) that ensures both stability of the closed-loop system and high-accuracy tracking. In our proposed approach, we use GPs to approximate the error between the commanded acceleration and the actual acceleration of the system, and then use the predicted mean and variance of the GP to calculate an upper bound on the uncertainty of the linearization. This uncertainty bound is then used in a robust, outer-loop controller to ensure stability of the overall system. Moreover, we show that using our proposed strategy, the tracking error converges to a ball with a radius that can be made arbitrarily small through appropriate control design. Furthermore, we verify the effectiveness of the proposed approach via simulations on (i) a 2 degree-of-freedom (DOF) planar manipulator, and (ii) a 6 DOF industrial manipulator using the Gazebo simulator.
In @cite_1 @cite_14 , GPs are utilized to learn the errors in the output torques of the inverse dynamics model online. In @cite_1 , the GP learning is combined with a state-of-the-art gradient descent method for learning feedback terms online. The main idea behind this approach is that the gradient descent method would correct for fast perturbations, while the GP is responsible for correcting slow perturbations. This allows for exponential smoothing of the GP hyperparameters, which increases the robustness of the GP at the cost of having slower reactiveness. Nevertheless, @cite_1 does not provide a proof of the robust stability of the closed-loop system. @cite_14 , the variance of the GP prediction is utilized to adapt the parameters of an outer-loop PD controller online, and the uniform ultimate boundedness of the tracking error is proved under some assumptions on the structure of the PD controller (e.g., the gain matrix was assumed to be diagonal, which imposes a decentralized gain control scheme). The results of @cite_14 are verified via simulations on a 2 DOF manipulator.
@cite_14 @cite_1
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Learning of inverse dynamics modeling errors is key for compliant or force control when analytical models are only rough approximations. Thus, designing real time capable function approximation algorithms has been a necessary focus towards the goal of online model learning. However, because these approaches learn a mapping from actual state and acceleration to torque, good tracking is required to observe data points on the desired path. Recently it has been shown how online gradient descent on a simple modeling error offset term to minimize tracking at acceleration level can address this issue. However, to adapt to larger errors a high learning rate of the online learner is required, resulting in reduced compliancy. Thus, here we propose to combine both approaches: The online adapted offset term ensures good tracking such that a nonlinear function approximator is able to learn an error model on the desired trajectory. This, in turn, reduces the load on the adaptive feedback, enabling it to use a lower learning rate. Combined this creates a controller with variable feedback and low gains, and a feedforward model that can account for larger modeling errors. We demonstrate the effectiveness of this framework, in simulation and on a real system. This paper introduces a learning-based robust control algorithm that provides robust stability and performance guarantees during learning. The approach uses Gaussian process (GP) regression based on data gathered during operation to update an initial model of the system and to gradually decrease the uncertainty related to this model. Embedding this data-based update scheme in a robust control framework guarantees stability during the learning process. Traditional robust control approaches have not considered online adaptation of the model and its uncertainty before. As a result, their controllers do not improve performance during operation. Typical machine learning algorithms that have achieved similar high-performance behavior by adapting the model and controller online do not provide the guarantees presented in this paper. In particular, this paper considers a stabilization task, linearizes the nonlinear, GP-based model around a desired operating point, and solves a convex optimization problem to obtain a linear robust controller. The resulting performance improvements due to the learning-based controller are demonstrated in experiments on a quadrotor vehicle. Learning in real-time applications, e.g., online approximation of the inverse dynamics model for model-based robot control, requires fast online regression techniques. Inspired by local learning, we propose a method to speed up standard Gaussian Process regression (GPR) with local GP models (LGP). The training data is partitioned in local regions, for each an individual GP model is trained. The prediction for a query point is performed by weighted estimation using nearby local models. Unlike other GP approximations, such as mixtures of experts, we use a distance based measure for partitioning of the data and weighted prediction. The proposed method achieves online learning and prediction in real-time. Comparisons with other nonparametric regression methods show that LGP has higher accuracy than LWPR and close to the performance of standard GPR and nu-SVR. Learning in real-time applications, e.g., online approximation of the inverse dynamics model for model-based robot control, requires fast online regression techniques. Inspired by local learning, we propose a method to speed up standard Gaussian process regression (GPR) with local GP models (LGP). The training data is partitioned in local regions, for each an individual GP model is trained. The prediction for a query point is performed by weighted estimation using nearby local models. Unlike other GP approximations, such as mixtures of experts, we use a distance based measure for partitioning of the data and weighted prediction. The proposed method achieves online learning and prediction in real-time. Comparisons with other non-parametric regression methods show that LGP has higher accuracy than LWPR and close to the performance of standard GPR and ν-SVR.