Solving the Time-Jerk Optimal Trajectory Planning Problem of a Robot Using Augmented Lagrange Constrained Particle Swarm Optimization

The problem of minimum time-jerk trajectory planning for a robot is discussed in this paper. The optimal objective function is composed of two segments along the trajectory, which are the proportional to the total execution time and the proportional to the integral of the squared jerk (which denotes the derivative of the acceleration). The augmented Lagrange constrained particle swarm optimization (ALCPSO) algorithm, which combines the constrained particle swarm optimization (CPSO) with the augmented Lagrangemultiplier (ALM) method, is proposed to optimize the objective function. In this algorithm, falling into a local best value can be avoided because a newparticle swarmis generated per initial procedure, and the best value gained fromthe former generation is saved and delivered to the next generation during the iterative search procedure to enable the best value to be found more easily and more quickly. Finally, the proposed algorithm is tested on a planar 3-degree-of-freedom (DOF) robot; the simulation results show that the algorithm is effective, offering a solution to the time-jerk optimal trajectory planning problem of a robot under nonlinear constraints.