Motion planning and collision avoidance using navigation vector fields

This paper presents a novel method on the motion and path planning for unicycle robots in environments with static circular obstacles. The method employs a family of 2-dimensional analytic vector fields, which have singular points of high-order type and whose integral curves exhibit various patterns depending on the value of a parameter λ. More specifically, for a known value of λ the vector field has a unique singular point of dipole type and its integral curves are suitable for steering the unicycle to a goal configuration. Furthermore, for the value of λ that the vector field has a continuum of singular points, the integral curves can be used to define flows around circular obstacles. An almost global feedback motion plan is then constructed by suitably blending attractive and repulsive vector fields in a static obstacle environment. The proposed motion planning and control design is also extended to the multi-agent case, where each agent needs to converge to a desired configuration while avoiding collisions with other agents. The efficacy of the approach is demonstrated via simulation results.