Collision-Free Trajectory Optimization for 2-Link Flexible Arm

Abstract

We propose a method of collision-free trajectory optimization for a 2-link flexible robot arm by using the optimal control theory. This method has following advantages: First, we can adopt some performance index concerning the driving energy, the arm vibration and so on; Second, we can restrict the state variable at the final time so that the vibration of the link stops at that time. We can get the optimal input signal as time function. This collision-free problem is the nonlinear optimal control problem with state variable inequality constraints. We apply a penalty function and get an ordinary two-point-boundary value problem. The simulation results show the optimal collision-free trajectory.