Path Planning for Mobile Objects in Four-Dimension Based on Particle Swarm Optimization Method with Penalty Function

Abstract EN

We present one algorithm based on particle swarm optimization (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.