An Application of Receding-Horizon Neural Control in Humanoid Robotics

Abstract

: Optimal trajectory planning of a humanoid arm is addressed. The goal is to make the end effector reach a desired target or track it when it moves in the arm's workspace unpredictably. As a reference setup, we considered a 7 degrees of freedom humanoid robot arm. Physical constraints require the online computations to be very quick. Following previous studies [1], a recedinghorizon 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, in the off-line phase, a set of neural networks (corresponding to the control functions over a finite horizon) is optimized using the Extended Ritz Method. The training set corresponds to a sampling of the arm and target position and velocity configuration space. 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 [5]. Once solved the off-line finite-horizon problem, 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.

Approximate optimal control for reaching and trajectory planning in a humanoid robot

“…-see [23]) yields the proper control at each time instant. The feasibility of this approach has already been tested on the control of a thrusts-actuated non-holonomic robot [18], while numerical results showing its effectiveness for different cost functions were presented in [22], for the motion of a simpler planar manipulator.…”