A Semismooth Predictor Corrector Method for Real-Time Constrained Parametric Optimization with Applications in Model Predictive Control

Real-time optimization problems are ubiquitous in control and estimation, and are typically parameterized by incoming measurement data and/or operator commands. This paper proposes solving parameterized constrained nonlinear programs using a semismooth predictor-corrector (SSPC) method. Nonlinear complementarity functions are used to reformulate the first order necessary conditions of the optimization problem into a parameterized non-smooth root-finding problem. Starting from an approximate solution, a semismooth Euler-Newton algorithm is proposed for tracking the trajectory of the primal-dual solution as the parameter varies over time. Active set changes are naturally handled by the SSPC method, which only requires the solution of linear systems of equations. The paper establishes conditions under which the solution trajectories of the root-finding problem are well behaved and provides sufficient conditions for ensuring boundedness of the tracking error. Numerical case studies featuring the application of the SSPC method to nonlinear model predictive control are reported and demonstrate the advantages of the proposed method

Youla-Kucera parameterized adaptive tracking control for optical data storage systems

In the next generation optical data storage systems, the tolerance of the tracking error will become even smaller under various unknown working situations. However, the unknown external disturbances caused by vibrations make it difficult to maintain the desired tracking precision during normal disk operation. It is proposed in this paper to use an adaptive regulation approach to maintain the tracking error below its desired value despite these unknown disturbances. The design of the regulator is formulated by augmenting a base controller into a Youla-Kucera (Q) parameterized set of stabilizing controllers so that both the deterministic and the random disturbances can be deal with properly. The adaptive algorithm is developed to search the desired Q parameter which satisfies the Internal Model Principle and thus the exact regulation against the unknown deterministic disturbance can be achieved. The performance of the proposed control approach is evaluated with experimental results that illustrate the capability of the proposed adaptive regulator to attenuate the unknown disturbances and achieve the desired tracking precision

Learning Task Priorities from Demonstrations

Bimanual operations in humanoids offer the possibility to carry out more than one manipulation task at the same time, which in turn introduces the problem of task prioritization. We address this problem from a learning from demonstration perspective, by extending the Task-Parameterized Gaussian Mixture Model (TP-GMM) to Jacobian and null space structures. The proposed approach is tested on bimanual skills but can be applied in any scenario where the prioritization between potentially conflicting tasks needs to be learned. We evaluate the proposed framework in: two different tasks with humanoids requiring the learning of priorities and a loco-manipulation scenario, showing that the approach can be exploited to learn the prioritization of multiple tasks in parallel.Comment: Accepted for publication at the IEEE Transactions on Robotic

Actor-Critic Reinforcement Learning for Control with Stability Guarantee

Reinforcement Learning (RL) and its integration with deep learning have achieved impressive performance in various robotic control tasks, ranging from motion planning and navigation to end-to-end visual manipulation. However, stability is not guaranteed in model-free RL by solely using data. From a control-theoretic perspective, stability is the most important property for any control system, since it is closely related to safety, robustness, and reliability of robotic systems. In this paper, we propose an actor-critic RL framework for control which can guarantee closed-loop stability by employing the classic Lyapunov's method in control theory. First of all, a data-based stability theorem is proposed for stochastic nonlinear systems modeled by Markov decision process. Then we show that the stability condition could be exploited as the critic in the actor-critic RL to learn a controller/policy. At last, the effectiveness of our approach is evaluated on several well-known 3-dimensional robot control tasks and a synthetic biology gene network tracking task in three different popular physics simulation platforms. As an empirical evaluation on the advantage of stability, we show that the learned policies can enable the systems to recover to the equilibrium or way-points when interfered by uncertainties such as system parametric variations and external disturbances to a certain extent.Comment: IEEE RA-L + IROS 202

Visual identification by signature tracking

We propose a new camera-based biometric: visual signature identification. We discuss the importance of the parameterization of the signatures in order to achieve good classification results, independently of variations in the position of the camera with respect to the writing surface. We show that affine arc-length parameterization performs better than conventional time and Euclidean arc-length ones. We find that the system verification performance is better than 4 percent error on skilled forgeries and 1 percent error on random forgeries, and that its recognition performance is better than 1 percent error rate, comparable to the best camera-based biometrics