Algorithmization of Constrained Motion for Car-Like Robots Using the VFO Control Strategy with Parallelized Planning of Admissible Funnels

Vehicles with car-like kinematics are ubiquitous, therefore an ability to algorithmize (i.e., how to plan and effectively execute) complex maneuvers in the presence of obstacles is vital to mobile robotics and intelligent vehicles. Traditionally, this problem is solved using the well known motion planning algorithms, which generate the open-loop control signals neglecting the effects of measurement noises, modeling uncertainties and imperfect robot actuation. While such effects can be compensated to some extent by online replanning, the application of feedback control algorithms to motion execution is unavoidable if robustness of the system is desired. Consequently, the recent works focus on integration of both motion planning and control algorithms to obtain motion plans robust to uncertainty of the initial conditions. In accordance with this trend, we propose a modified VFO (Vector Field Orientation) control law, which is designed to satisfy the state and input constraints resulting from the presence of obstacles in the environment, respect the steering angle limits in conjunction with steering dynamics of the car-like robot, and preserve continuity of the control input signals. Thanks to analytic characterization of admissible funnels (i.e. positively invariant subsets of the configuration space) developed from an analysis of the VFO control law, we guarantee satisfaction of all the mentioned constraints in the continuous domains of time and configuration space of the robot without sacrificing computational efficiency of the planning process. A specific funnel is planned with a highly parallelized deterministic sampling-based algorithm achieving quasi-real-time performance.