Decentralized Multiagent Trajectory Planning

Abstract

In this work, we present novel approaches to solve the decentralized trajectory planning for networked multiagent systems. We first provide the new reformulation of the safety constraint for faster convergence with guaranteed safety, with the iteration to converge being a fraction of traditional linearization approaches. This newly proposed constraint reformulation is based on the combination of the dual problem to the minimum distance between convex sets and biconvex optimization. The second important result obtained is the fully decentralized, scalable trajectory optimization algorithm based on the reformulated biconvex optimization, along with the successive convexification (SCVX) for handling the nonlinear dynamics. This algorithm features a minimum sharing data in comparison to the traditional distributed gradient method or dual decomposition-based algorithm like alternating direction method of multipliers (ADMM). The number of variables shared is less than half that of ADMM-SCP in our setups. We also showed the strong convergence of our biconvex method to the partial minimum under mild assumptions. Numerical results with up to ten agents and hardware experiments were performed to validate our claims. This work will enable efficient coordination of large-scale cooperating unmanned vehicles navigating in complex environments.