A Smooth Reformulation of Collision Avoidance Constraints in Trajectory Planning

This work describes a novel, computational-cost-reducing collision avoidance constraint for trajectory planning of robotic systems through adopting a smooth approximation of the maximum function. The proposed method reduces the number of constraints in a trajectory planning problem by expressing a number of constraints as one single constraint that is approximately equivalent to the most critical constraint. This reformulation lowers planning times while still maintaining identical guarantees on collision avoidance as a traditional approach. Although this paper focuses on collision avoidance constraints, the presented approach can easily be extended towards other constraints. The algorithm is numerically validated on three cases, both in two and three dimensional environments. It is compared in terms of computational efficiency with a traditional trajectory planner where all collision avoidance constraints are treated separately. The presented results show a promising improvement in performance of trajectory planning for robotic applications.