Planning with Differential Constraints Application to Navigation of Wheeled Mobile Robots on Uneven Terrain and in Dynamic Environments

Abstract

This thesis deals with motion planning problem with differential inequality and equality constraints. The evolution model of the wheeled mobile robots are usually described as differential equality constraints. Whereas higher level requirements are modelled as differential inequality constraints. Stability requirements for a wheeled mobile robot operating on uneven terrains can be represented as set of differential inequalities. Similarly the collision avoidance requirements for a robot operating in dynamic environments are also modelled as differential inequality constraints. In this thesis we propose computationally efficient methodologies for computing the solution space of differential constraints. We show that we are able to obtain a characterization of solution spaces by just solving a set of low dimensional linear and quadratic inequalities. Consequently we build on top of this result and propose incremental sampling based planners as well as trajectory optimization approaches for motion planning. newline newlineAt the secondary level, contributions to some specific aspects of motion planning on uneven terrain and in dynamic environments are made. Existing works on uneven terrain navigation are based on planar or point mass evolution model of the robot. In the current thesis we present the methodology to deduce the 3D evolution of the robot on uneven terrain. We also present a novel concept called Feasible Acceleration Count which acts as an unified metric for quantifying the stability of the robot on uneven terrain as well as the efficiency of the incremental sampling based planners on producing stable trajectories on uneven terrain. We also present a novel concept called time scaled collision cone which is path constrained version of the collision cone concept used to characterize the set of collision avoidance manoeuvres in dynamic environments. We show that time scaled collision cone constrains can be solved in closed form and forms the crux of the proposed motion planning framework for dynamic environments.