Path planning for mobile objects in four-dimension based on particle swarm optimization method with penalty function

Abstract

We present one algorithmbased on particle swarmoptimization (PSO) with penalty function to determine the conflict-free path for mobile objects in four-dimension (three spatial and one-time dimensions) with obstacles. The shortest path of the mobile object is set as goal function, which is constrained by conflict-free criterion, path smoothness, and velocity and acceleration requirements. This problem is formulated as a calculus of variation problem (CVP). With parametrization method, the CVP is converted to a time-varying nonlinear programming problem (TNLPP). Constraints of TNLPP are transformed to general TNLPP without any constraints through penalty functions.Then, by using a little calculations and applying the algorithm PSO, the solution of the CVP is consequently obtained. Approach efficiency is confirmed by numerical examples. Copyright © 2013 Yong Ma et al.