Constrained multi-objective trajectory planning of parallel kinematic machines

This paper presents a new approach to multi-objective dynamic trajectory planning of parallel kinematic machines (PKM) under task, workspace and manipulator constraints. The robot kinematic and dynamic model, (including actuators) is first developed. Then the proposed trajectory planning system is introduced. It minimizes electrical and kinetic energy, robot traveling time separating two sampling periods, and maximizes a measure of manipulability allowing singularity avoidance. Several technological constraints such as actuator, link length and workspace limitations, and some task requirements, such as passing through imposed poses are simultaneously satisfied. The discrete augmented Lagrangean technique is used to solve the resulting strong nonlinear constrained optimal control problem. A decoupled formulation is proposed in order to cope with some difficulties arising from dynamic parameters computation. A systematic implementation procedure is provided along with some numerical issues. Simulation results proving the effectiveness of the proposed approach are given and discussed.