Mathematical programming for multi-vehicle motion planning under communication constraints

Abstract

Multi-Vehicle Motion Planning (MVMP) problems feature multiple vehicles traversing in their work space while avoiding collisions with each other and with other obstacles. Real world MVMP problems require the optimization of suitable performance measures under an array of constraints including kinematics, dynamics, communication connectivity, target tracking, and collision avoidance. The general MVMP problem can thus be formulated as a mathematical program (MP). In this thesis we present a mathematical programming framework that captures the salient features of the general MVMP problem. We use state-of-the-art solution algorithms and associated numerical solvers developed by our group to solve MVMP problems using this framework.To demonstrate the effectiveness of this framework, we investigate a variant of the general MVMP problem, viz. Multi-Vehicle Path Coordination wherein we generate time optimal velocity profiles for multiple robotic vehicles confined to move along predetermined and fixed paths. Each robot must follow a fixed and known path, arrive at its goal as quickly as possible (or at least not increase the time for the last robot to arrive at its goal) and stay in communication with other robots in the arena throughout its journey. We enforce a variety of communication connectivity constraints that incorporate deterministic and stochastic physical layer communication models to ensure that the robots can communicate with each other while in transit. We develop Partition Elimination constraints that assist in ensuring that the communication network is fully connected while the robots are in transit. The resulting mathematical programming models are solved using state-of-the-art highly efficient mixed integer nonlinear optimization tools developed by our group. Several conditions that affect the feasibility of the problem are identified and formalized.Both centralized and decentralized formulations are studied to demonstrate (i) the effect of communication connectivity requirements on robot velocity profiles; (ii) the dependence of the scenario completion time on communication connectivity requirements; (iii) the dependence of computation time on the number of robots; (iv) the tradeoff between the arrival time and the communication connectivity requirements. As MP solution algorithms and associated numerical solvers continue to develop, we anticipate that MP solution techniques will be applied to an increasing number of MVMP problems and this thesis may serve as a guide for future MVMP research.%%%%Ph.D., Electrical Engineering – Drexel University, 2011