Motion Planning for Nonlinear Symmetric Distributed Robotic Formations

Abstract

This paper develops a motion planning algorithm which exploits symmetries in distributed systems to reduce motion planning computation complexity. Symmetries allow for algebraic manipulations that are computationally costly, which normally must be carried out for each component in a distributed system, to be related among various symmetric components in a distributed system by a simple algebraic relationship. This leads to a large reduction in the complexity of the overall motion planning problem for a group of distributed mobile robotic agents. In particular, due to the manner in which a symmetric system is defined, the structure of the Chen—Fliess—Sussmann differential equations has a simple relationship among various symmetric components of a distributed system. Essentially, symmetries are defined in a manner which preserves the Lie algebraic structure of each component. In a system with distributed computational capability, the motion planning computations may be distributed throughout formation in such a way that the objectives of the formation are satisfied and collision avoidance is guaranteed. The algorithm maintains a rigid body formation at the beginning and end of the trajectory, as well as possibly specified intermediate points. Due to the generally nonholonomic nature of mobile robots, guaranteeing a rigid body formation during the intermediate motion is impossible. However, it is possible to bound the magnitude of the deviation from the rigid body formation at any point along the trajectory. Simulation and experimental results are provided to demonstrate the utility of the algorithm.