Collision-free trajectory planning for unmanned vehicles using sequential second-order cone programming

This paper addresses the trajectory planning problem for unmanned vehicles with free terminal time in constrained environments with obstacles. A variable substitution method is employed to handle the free terminal time, transforming the nonconvex cost function and constraints into convex forms while maintaining feasibility. For obstacle avoidance, we propose a Chebyshev-node based discretization method that focuses on the vertices of vehicles and obstacles modeled as convex polygons, along with a convexification approach for volumetric obstacle avoidance. The optimization problem is solved within a sequential convex programming framework by converting it into a series of second-order cone programming subproblems, enhancing real-time performance. The effectiveness and computational efficiency of the proposed method are validated through numerical simulations and comparisons with other methods.