Robust Parafoil Terminal Guidance Using Massively Parallel Processing

Abstract

Terminal guidance of autonomous parafoils is a difficult problem in which wind uncertainty and system underactuation are major challenges. Existing strategies almost exclusively use impact error as the criterion for optimality. Practical airdrop systems, however, must also include other criteria that may be even more important than impact error in some missions, such as ground speed at impact or constraints imposed by challenging dropzones. Furthermore, existing guidance schemes determine terminal trajectories using deterministic wind information and may result in a solution that works in ideal wind but may be sensitive to variations. The work described here develops a guidance strategy that uses massively parallel Monte Carlo simulation performed on a graphics processing unit to rank candidate trajectories in terms of robustness to wind uncertainty. Based on the guidance system's confidence in wind estimates, an appropriate trajectory path is chosen that provides a reasonable level of robustness given uncertainty in wind conditions. The result is robust guidance, as opposed to optimal guidance. Through simulation results, the proposed path planning scheme proves more robust in realistic dynamic wind environments compared with previous optimal trajectory planners that assume perfect knowledge of a constant wind. Nomenclature A, B, C = discrete system state space matrices B = discrete model control sensitivity D = distance of the turn initial point with respect to the target H p = discrete prediction horizon i T , j T , k T = target frame unit vectors L = distance to target along target line Q, R = positive semi-definite error and control penalty matrices r = parafoil yaw rate R = final turn radius t 0 = time final turn begins t 1 = time final approach begins t 2 = time of predicted impact T app , des app T = final approach time and desired final approach time t pre = final turn advance timing U = discrete optimal control vector h V , v V = parafoil horizontal and vertical speed W x , W y = target frame wind speed components x, y, z = parafoil inertial positions in the target frame x = parafoil model state vector δ a = parafoil asymmetric brake deflection ∆ = predictive controller discrete sampling period