Box Particle Control for Aerospace Vehicles Guidance Under Failure Probability Constraints

Determining a constrained optimal trajectory remains tricky when the state suffers non-analytical uncertainty and when the feasible set is non-convex. This paper presents a chance constrained trajectory planning approach, called Box Particle Control (BPC), which guarantees an a priori specified maximum probability of constraints violation along a predicted trajectory. This failure probability is estimated by approximating the state density with a mixture of bounded kernels, defined by weighted box particles, and is used as a constraint in an optimization scheme. Numerical simulations illustrate the performance of BPC, which ensures the constraints satisfaction even for low numbers of box particles. The BPC makes it possible to tackle non-analytic state densities (e.g., multimodalities) and non-convex feasible sets with a higher robustness and a 60% lower computational load than previous approaches in terms of number of elementary operations.