OC3: A Reactive Velocity Level Motion Planner with Complementarity Constraint-based Obstacle Avoidance for Mobile Robots

This paper presents a novel real-time motion planning method for differential drive mobile robots. Reactive planners, in the context of mobile robots, are usually vulnerable to challenges like local minima, differential constraint satisfaction, and dynamic obstacles. To this end, we present the Off-Center point Complementarity Constraint (OC3) planner, which respects the differential constraints of robot kinematics, can handle dynamic obstacles, and is more robust to the local minima problem compared to traditional methods like artificial potential fields. Our OC3 planner utilizes a virtual contact mechanism at a distal off-center point of the robot for obstacle avoidance, thereby ensuring smooth maneuvers. We formulate the obstacle avoidance problem as a feasibility problem with complementarity constraints, and derive a closed-form solution. This enables fast online computation of collision-free waypoints for the robot off-center. Once a collision-free state of the off-center point is found, inverse velocity kinematics is used to compute the reference control input velocities (? R²) for the robot. We further show that OC3 can be used as a local planner in RRT type of sampling-based global planning framework to avoid the local minimum problem. Our extensive analysis through various case studies and rigorous simulation experiments, using the popular ROS based Turtlebot3 simulator, in the presence of static and dynamic obstacles, demonstrate the efficacy of our framework including real-time proficiency.