On-line time-optimal algorithm for manipulator trajectory planning

A near-optimal solution to the path-unconstrained time-optimal trajectory planning problem is addressed in this paper. While traditional trajectory planning strategies are entirely based on kinematic considerations, manipulator dynamics are neglected altogether. This often results in mathematically tractable solutions which do not maximise the performance that manipulators might be capable of at any given time. The strategy presented in this work has two distinguishing features. First, 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 the linearization approach taken and also the fundamental parameter uncertainty of the dynamic equations of motion. 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 maximising the capabilities of the device can lead to an overall improvement in the manipulator time response of up to 25-30%.