An Application of Receding-Horizon Neural Control in Humanoid Robotics

Abstract

Optimal trajectory planning of a humanoid arm is addressed. The reference setup is the humanoid robot James [1]. The goal is to make the end effector reach a desired target or track it when it moves in the arm’s workspace unpredictably. Physical constraints and setup capabilities prevent us to compute the optimal control online, so an off-line explicit control is required. Following previous studies [2], a receding-horizon method is proposed that consists in assigning the control function a fixed structure (e.g., a feedforward neural network) where a fixed number of parameters have to be tuned. More specifically a set of neural networks (corresponding to the control functions over a finite horizon) is optimized using the Extended Ritz Method. The expected value of a suitable cost is minimized with respect to the free parameters in the neural networks. Therefore, a nonlinear programming problem is addressed that can be solved by means of a stochastic gradient technique. The resulting approximate control functions are sub-optimal solutions, but (thanks to the well-established approximation properties of the neural networks) one can achieve any desired degree of accuracy [3]. Once the off-line finite-horizon problem is solved, only the first control function is retained in the on-line phase: at any sample time t, given the system’s state and the target’s position and velocity, the control action is generated with a very small computational effort.