Feasibility and coordination of multiple mobile vehicles with mixed equality and inequality constraints

TL;DR

This paper presents a comprehensive framework for coordinating multiple vehicles with diverse constraints using differential-algebraic equations and viability theory, including heuristic trajectory generation and analytical solutions for simple cases.

Contribution

It introduces a general approach to assess and achieve feasible multi-vehicle coordination under heterogeneous dynamics and constraints, with new analytical solutions and validation through simulations.

Findings

Feasibility conditions for multi-vehicle coordination are established.

A heuristic algorithm effectively generates feasible trajectories.

Analytical solutions serve as benchmarks for simple vehicle groups.

Abstract

We consider the problem of feasible coordination control for multiple homogeneous or heterogeneous mobile vehicles subject to various constraints (nonholonomic motion constraints, holonomic coordination constraints, equality/inequality constraints etc). We develop a general framework involving differential-algebraic equations and viability theory to describe and determine coordination feasibility for a coordinated motion control under heterogeneous vehicle dynamics and different types of coordination constraints. If a solution exists for the derived differential-algebraic equations and/or inequalities, a heuristic algorithm is proposed for generating feasible trajectories for each individual vehicle. In case studies on coordinating two vehicles, we derive analytical solutions to motion generation for two-vehicle groups consisting of car-like vehicles, unicycle vehicles, or vehicles with constant speeds, which serve as benchmark coordination tasks for more complex vehicle groups. We show several simulation experiments on multi-vehicle coordination under various constraints to validate the theory and the effectiveness of the proposed schemes.