Optimal Motion Planning of Manipulators With Elastic Links and Joints in Generalized Point-to-Point Task

摘要

Finding optimal trajectory is critical in several applications for robots from payload transport between two given states in a prescribed time such that a cost functional is minimized. This paper is concerned with the path planning of flexible robotic arms in point-to-point motion, based on indirect solution of optimal control problem. Dynamic modelling technique based on the combined Euler–Lagrange formulation and assumed modes method is applied, then by implementing the Pontryagin’s minimum principle; necessary conditions for optimality are derived. Nonlinear states and control constraints are treated without any simplifications or transforming them into sequences of systems with linear equations. By these means, the modelling of the complete optimal control problem and the accompanying boundary value problem is automated to a great extent. Finally, the performance of method is illustrated through the computer simulations.