Sampling-based Motion Planning via Control Barrier Functions

Robot motion planning is central to real-world autonomous applications, such as self-driving cars, persistence surveillance, and robotic arm manipulation. One challenge in motion planning is generating control signals for nonlinear systems that result in obstacle free paths through dynamic environments. In this paper, we propose Control Barrier Function guided Rapidly-exploring Random Trees (CBF-RRT), a sampling-based motion planning algorithm for continuoustime nonlinear systems in dynamic environments. The algorithm focuses on two objectives: efficiently generating feasible controls that steer the system toward a goal region, and handling environments with dynamical obstacles in continuous time. We formulate the control synthesis problem as a Quadratic Program (QP) that enforces Control Barrier Function (CBF) constraints to achieve obstacle avoidance. Additionally, CBF-RRT does not require nearest neighbor or explicit collision checks during sampling.

[1]  B. Faverjon,et al.  Probabilistic Roadmaps for Path Planning in High-Dimensional Con(cid:12)guration Spaces , 1996 .

[2]  Emilio Frazzoli,et al.  Sampling-based algorithms for optimal motion planning , 2011, Int. J. Robotics Res..

[3]  Robert Platt,et al.  Optimal sampling-based planning for linear-quadratic kinodynamic systems , 2013, 2013 IEEE International Conference on Robotics and Automation.

[4]  Hung Manh La,et al.  Dynamic path planning and replanning for mobile robots using RRT , 2017, 2017 IEEE International Conference on Systems, Man, and Cybernetics (SMC).

[5]  L. Leemis.  Applied Linear Regression Models , 1991 .

[6]  Mo Chen,et al.  FaSTrack: A modular framework for fast and guaranteed safe motion planning , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[7]  Nahum Shimkin,et al.  Nonlinear Control Systems , 2008 .

[8]  Aaron D. Ames,et al.  Control barrier function based quadratic programs with application to bipedal robotic walking , 2015, 2015 American Control Conference (ACC).

[9]  Calin Belta,et al.  Control Barrier Functions for Systems with High Relative Degree , 2019, 2019 IEEE 58th Conference on Decision and Control (CDC).

[10]  Koushil Sreenath,et al.  Exponential Control Barrier Functions for enforcing high relative-degree safety-critical constraints , 2016, 2016 American Control Conference (ACC).

[11]  J. How,et al.  Receding horizon path planning with implicit safety guarantees , 2004, Proceedings of the 2004 American Control Conference.

[12]  J. Neter,et al.  Applied Linear Regression Models , 1983 .

[13]  Paulo Tabuada,et al.  Control barrier function based quadratic programs with application to adaptive cruise control , 2014, 53rd IEEE Conference on Decision and Control.

[14]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[15]  S. LaValle.  Rapidly-exploring random trees : a new tool for path planning , 1998 .

[16]  Li Wang,et al.  Control Barrier Certificates for Safe Swarm Behavior , 2015, ADHS.

[17]  Jur P. van den Berg,et al.  Kinodynamic RRT*: Asymptotically optimal motion planning for robots with linear dynamics , 2013, 2013 IEEE International Conference on Robotics and Automation.

[18]  Olzhas Adiyatov,et al.  A novel RRT*-based algorithm for motion planning in Dynamic environments , 2017, 2017 IEEE International Conference on Mechatronics and Automation (ICMA).

[19]  Leslie Pack Kaelbling,et al.  LQR-RRT*: Optimal sampling-based motion planning with automatically derived extension heuristics , 2012, 2012 IEEE International Conference on Robotics and Automation.