Real-time optimal trajectory planning for robotic manipulators with functional redundancy

In this paper we show that by allowing a small orientation error in the specifications of the end effector orientation for spray paint applications, both speed and performance can be substantially improved. In previous publications, we have shown how a continuous set of orientations can be represented as a positive definiteness test on a given matrix. This allows us to cast the problem into a convex optimisation problem where the optimal orientation for each time step is to be found. The orientation which allows the manipulator to follow a given path as fast as possible and with constant speed is considered the optimal orientation. In this paper we show how to solve this problem for every time step. The solution is computationally fast and can be implemented in real time. Numerical examples are presented to verify the efficiency of the approach.