Improved Intersample Avoidance Constraints for Mixed-Integer Motion Planning of Differential Drive Micromobility Vehicles

Abstract

This paper addresses the problem of intersample collision avoidance for mixed-integer motion planners on differential drive micromobility platforms. We employ a Mixed-Integer Linear Programming (MILP) formulation to generate time and energy-efficient maneuvers for a vehicle in pick-up and delivery tasks. MILP-based motion planners have been widely employed due to their capability to handle the nonconvexity of trajectory generation problems, explicitly minimize objectives such as mission completion time, and incorporate logical constraints often used to encode high-level decision-making in autonomous systems. However, they also typically require explicit intersample collision avoidance constraints to prevent the resulting trajectories from intercepting obstacles between planning steps. Existing solutions for this problem rely on sufficient conditions that can lead to overly conservative maneuvers. Two novel constraints, based on the concepts of intermediary points (IP) and line search (LS), were devised to address this issue with reduced conservatism, with the latter being specifically tailored for platforms with differential drive kinematics. We evaluated these formulations against a classical baseline using Monte Carlo simulations and statistical analysis. The results revealed that both methods yield more efficient maneuvers than the baseline in terms of a cost comprised of control effort and completion time, with the LS approach consistently providing the best solutions and the IP method being applicable to a wider range of vehicles. The evaluations also revealed that the novel methods introduced additional complexity to the model, resulting in increased computation times. We therefore concluded that the proposed formulations are ideal for scenarios where efficiency is paramount and lower replanning frequencies are acceptable. Furthermore, we discussed strategies to mitigate this computational overhead, potentially enabling the integration of the novel constraints into receding horizon schemes.