A Case Study of the Collision-Avoidance Problem Based on Bernstein–Bézier Path Tracking for Multiple Robots with Known Constraints

In this paper a case study of a new, cooperative, collision-avoidance method for multiple, nonholonomic robots based on Bernstein–Bézier curves is given. In the presented examples the velocities and accelerations of the mobile robots are constrained and the start and the goal velocity are defined for each robot. This means that the proposed method can be used as a subroutine in a huge path-planning problem in real time, in a way to split the whole path into smaller partial paths. The reference path of each robot, from the start pose to the goal pose, is obtained by minimizing the penalty function, which takes into account the sum of all the path lengths subjected to the distances between the robots, which should be bigger than the minimum distance defined as the safety distance, and subjected to the velocities and accelerations which should be lower than the maximum allowed for each robot. When the reference paths are defined the model-predictive trajectory tracking is used to define the control. The prediction model derived from the linearized tracking-error dynamics is used to predict future system behavior. The control law is derived from a quadratic cost function consisting of the system tracking error and the control effort. The proposed method was tested with a simulation and with a real-time experiment in which four robots were used.

[1]  A. Ollero,et al.  Predictive path tracking of mobile robots. Application to the CMU NavLab , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[2]  Francesco Maria Raimondi,et al.  A new fuzzy robust dynamic controller for autonomous vehicles with nonholonomic constraints , 2005, Robotics Auton. Syst..

[3]  Madan M. Gupta,et al.  Adaptive navigation of mobile robots with obstacle avoidance , 1997, IEEE Trans. Robotics Autom..

[4]  Tsutomu Hasegawa,et al.  Space Reasoning from Action Observation for Motion Planning of Multi-Robots: Mutual Collision Avoidance in a Narrow Passage , 1996 .

[5]  Farzad Pourboghrat,et al.  Adaptive control of dynamic mobile robots with nonholonomic constraints , 2002, Comput. Electr. Eng..

[6]  Vijay Kumar,et al.  Control of Mechanical Systems With Rolling Constraints , 1994, Int. J. Robotics Res..

[7]  J. M. D. Silva,et al.  Model Predictive Control of a Mobile Robot Using Linearization , 2022 .

[8]  Gregor Klan Tracking-error model-based predictive control for mobile robots in real time , 2007 .

[9]  Antonio Bicchi,et al.  Path tracking control for Dubin's cars , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[10]  Mohan M. Trivedi,et al.  A neuro-fuzzy controller for mobile robot navigation and multirobot convoying , 1998, IEEE Trans. Syst. Man Cybern. Part B.

[11]  Dongbing Gu,et al.  Neural predictive control for a car-like mobile robot , 2002, Robotics Auton. Syst..

[12]  Ronald C. Arkin,et al.  Cooperation without communication: Multiagent schema-based robot navigation , 1992, J. Field Robotics.

[13]  Ching-Hung Lee,et al.  Tracking control of unicycle-modeled mobile robots using a saturation feedback controller , 2001, IEEE Trans. Control. Syst. Technol..

[14]  Fumio Kojima,et al.  Adaptive Behavior of Mobile Robot Based on Sensory Network. , 1999 .

[15]  Ilya Kolmanovsky,et al.  Developments in nonholonomic control problems , 1995 .

[16]  Fumio Miyazaki,et al.  A stable tracking control method for an autonomous mobile robot , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[17]  Marilena Vendittelli,et al.  WMR control via dynamic feedback linearization: design, implementation, and experimental validation , 2002, IEEE Trans. Control. Syst. Technol..

[18]  Julio E. Normey-Rico,et al.  A Smith-predictor-based generalised predictive controller for mobile robot path-tracking , 1998 .

[19]  Ichiro Suzuki,et al.  Distributed algorithms for formation of geometric patterns with many mobile robots , 1996, J. Field Robotics.

[20]  Claude Samson,et al.  Time-varying Feedback Stabilization of Car-like Wheeled Mobile Robots , 1993, Int. J. Robotics Res..