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

Online optimal planning of robotic arm movement is addressed. Optimality is inspired by computational models, where a “cost function” is used to describe limb motions according to different criteria. A method is proposed to implement optimal planning in Cartesian space, minimizing some cost function, by means of numerical approximation to a generalized nonlinear model predictive control problem. The Extended RItz Method is applied as a functional approximation technique. Differently from other approaches, the proposed technique can be applied on platforms with strict control temporal constraints and limited processing capability, since the computational burden is completely concentrated in an off-line phase. The trajectory generation on-line is therefore computationally efficient. Task to joint space conversion is implemented on-line by a closed loop inverse kinematics algorithm, taking into account the robot´s physical limits. Experimental results, where a 4DOF arm moves according to a particular nonlinear cost, show the effectiveness of the proposed approach, and suggest interesting future developments.