Abstract
This paper presents a decentralized zero-sum optimal control method for MRMs with environmental collisions via an actor-critic-identifier (ACI) structure-based adaptive dynamic programming (ADP) algorithm. The dynamic model of the MRMs is formulated via a novel collision identification method that is deployed for each joint module, in which the local position and torque information are used to design the model compensation controller. A neural network (NN) identifier is developed to compensate the model uncertainties and then, the optimal control problem of the MRMs with environmental collisions can be transformed into a two-player zero-sum optimal control one. Based on the ADP algorithm, the Hamilton-Jacobi-Isaacs (HJI) equation is solved by constructing the actor-critic NNs, thus making the derivation of the approximate optimal control policy feasible. Based on the Lyapunov theory, the closed-loop robotic system is proved to be asymptotically stable. Finally, the experiments are conducted to verify the effectiveness and advantages of the proposed method.
Highlights
Modular robot manipulators have attracted extensive attentions in robotics community since they have better structural adaptability and flexibility than conventional robot manipulators
To address the problems of enhancing the stability and control precision of the robot manipulator systems in the face of environmental collisions, collision identification, which aims at obtaining the collision joint torques, is considered an efficient method to implement the joint torque feedback and to facilitate the controller design of the robotic systems with collisions
Where xiυ denotes a determined neural network (NN) state; xυ = [xd, xiυ ]T = [x1d, x2d · · · xmd, xiυ ]T, m < i is as defined state vector that is composed of the NN state as well as the known and bounded reference robotic system states; wiυ is the unknown ideal NN weight; εiυ represents the finite NN approximation error; σiυ indicates the activation function that is selected as the following Gaussian function: σiυ = exp
Summary
Modular robot manipulators have attracted extensive attentions in robotics community since they have better structural adaptability and flexibility than conventional robot manipulators. The dynamic model of the MRM systems is formulated via a novel harmonic drive compliance model-based collision identification method, and a model-based compensation controller is developed by effectively utilizing the local position and torque information of each joint module. COLLISION IDENTIFICATION Collision identification aims at estimating the coupled torques of each robotic joint, while the uncertain environmental collisions are acting along the robot structure [45] In this part, a novel collision identification method is presented based on a nonlinear harmonic drive compliance model as well as the position and current measurements of each joint module. Based on the nonlinear harmonic drive compliance model, in this part, we focus on estimating the coupled joint torque, which equal to the flexspline output torque, when the environmental collision happened. The coupled joint torque is utilized in dynamic model formulation of MRMs
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