Modified formula for velocity and acceleration setting in Obstacle Avoidance problem

This paper concerns on an optimal control problem of a robot movement from an initial point to another target point while avoiding obstacles. Previous study had generated a trajectory that should be taken by the robot to minimized the consumed energy while moving with constant velocity. Here, we find the optimal performance index value which minimizes the trajectory length as well as the energy usage of the robot. We also consider nonconstant velocity which changes over time as the robot moves. The solution is generated numerically by using software package TOMLAB/PROPT. The results show that there is different route taken by the robot yet it is shorter in distance. Also, the optimum energy and trajectory length can be obtained by setting the right penalty values at both measures.