A near-optimal solution to the path-unconstrained time-optimal trajectory planning problem is described in this paper. While traditional trajectory planning strategies are entirely based on kinematic considerations, manipulator dynamics are usually neglected altogether. The strategy presented in this work has two distinguishing features. Firstly, the trajectory planning problem is reformulated as an optimal control problem, which is in turn solved using Pontryagin's maximum/minimum principle. This approach merges the traditional division of trajectory planning followed by trajectory tracking into one process. Secondly, the feedback form compensates for the dynamic approximation errors derived from linearization and the fundamental parameter uncertainty of the dynamic equations of motion. This approach can cope with flexible robots as well as rigid links. The terminal phase of the motion is controlled by a feedforward controller to reduce chatter vibrations. Results from simulations and an on-line implementation to a general-purpose open-chain industrial manipulator, the CRS A251, confirm the validity of the approach and show that maximizing the capabilities of the device can lead to an overall improvement in the manipulator time response of up to 24 per cent, while retaining an acceptable overshoot and steady state error regime.
Optimal Trajectory Planning of Grinding Robot Based on Improved Whale Optimization Algorithm
