Collision-free Source Seeking Control Methods for Unicycle Robots (2212.07203v4)
Abstract: In this work, we propose a collision-free source-seeking control framework for a unicycle robot traversing an unknown cluttered environment. In this framework, obstacle avoidance is guided by the control barrier functions (CBF) embedded in quadratic programming, and the source-seeking control relies solely on the use of onboard sensors that measure the signal strength of the source. To tackle the mixed relative degree and avoid the undesired position offset for the nonholonomic unicycle model, we propose a novel construction of a control barrier function (CBF) that can directly be integrated with our recent gradient-ascent source-seeking control law. We present a rigorous analysis of the approach. The efficacy of the proposed approach is evaluated via Monte-Carlo simulations, as well as, using a realistic dynamic environment with moving obstacles in Gazebo/ROS.
- S. Azuma, M.Sakar and G.J. Pappas, “Stochastic source-seeking by mobile robots,” IEEE Transactions on Automatic Control, vol. 57, no. 9, pp. 2308-2321, 2012.
- P. Ogren, E. Fiorelli, and N. E. Leonard, “Cooperative control of mobile sensor networks: Adaptive gradient climbing in a distributed environment,” IEEE Transactions on Automatic control, vol. 49, no. 8, pp. 1292-1302, 2004.
- JC. Knight, “Safety critical systems: challenges and directions,” Proc. 24th International Conference on Software Engineering, pp. 547-550, May 2002.
- N. Hovakimyan, C. Cao, E. Kharisov, E. Xargay, and I. Gregory, “L 1 adaptive control for safety-critical systems,” IEEE Control Systems Magazine, vol. 31, no. 5, pp. 54-104, 2001.
- R. Zou, V. Kalivarapu, E. Winer, J. Oliver and S. Bhattacharya, “Particle swarm optimization-based source seeking,” IEEE Transactions on Automation Science and Engineering, vol. 12, no. 3, pp. 865-875, 2015.
- D. Baronov, J. Baillieul, “Autonomous vehicle control for ascending/descending along a potential field with two applications,” Proc. 2008 IEEE American Control Conference, pp. 678-683, June 2008.
- BP. Huynh, CW. Wu and YL. Kuo, “Force/Position hybrid control for a hexa robot using gradient descent iterative learning control algorithm,” IEEE Access ,vol. 7, pp. 72329-72342, 2019.
- DE. Soltero, M. Schwager and D. Rus, “Decentralized path planning for coverage tasks using gradient descent adaptive control,” The International Journal of Robotics Research, vol. 33, no. 3, pp. 401-25, 2014.
- J. Cortés, “Distributed gradient ascent of random fields by robotic sensor networks,” Proc. 46th IEEE Conference on Decision and Control, pp. 3120-3126, 2007.
- M. Ghadiri-Modarres, M. Mojiri, “Normalized Extremum Seeking and its Application to Nonholonomic Source Localization,” IEEE Transactions on Automatic Control, in-press, 2020.
- HB. Dürr, MS. Stanković, C. Ebenbauer, KH. Johansson, “Lie bracket approximation of extremum seeking systems,” Automatica, vol. 49, no. 6, pp. 1538-52, 2013.
- HB. Dürr, M. Krstić, A. Scheinker, C. Ebenbauer, “Extremum seeking for dynamic maps using Lie brackets and singular perturbations,” Automatica, vol. 83, pp. 91-99, 2017.
- C. Zhang, D. Arnold, N. Ghods, A. Siranosian, M. Krstic, “Source seeking with non-holonomic unicycle without position measurement and with tuning of forward velocity,” Systems & Control Letters, vol. 56, no. 3, pp. 245-252, 2007.
- N. Ghods, and M. Krstic, “Speed regulation in steering-based source seeking,” Automatica, vol. 46, no. 2, pp. 452-459, 2010.
- J. Cochran, M. Krstic, “Nonholonomic source seeking with tuning of angular velocity,” IEEE Trans. Automatic Control, vol. 54, no. 4, pp. 717-731, 2009.
- A. Raisch and M. Krstić, “Overshoot-free steering-based source seeking,” IEEE Transactions on Control Systems Technology, vol. 25, pp. 818-827, 2016.
- S. Liu and M. Krstic, “Stochastic source seeking for nonholonomic unicycle,” Automatica, vol. 46, no. 9, pp. 1443-1453, 2010.
- J. Lin, S. Song, K. You, M. Krstic, “Stochastic source seeking with forward and angular velocity regulation,” Automatica, vol. 83, pp. 378-386, 2017.
- S. Azuma, M.S. Sakar and G.J. Pappas, “Stochastic source seeking by mobile robots,” IEEE Transactions on Automatic Control, vol. 57, no. 9, pp. 2308-2321, 2012.
- Y. Landa, N. Tanushev and R. Tsai, “Discovery of point sources in the Helmholtz equation posed in unknown domains with obstacles,” Communications in Mathematical Sciences, vol. 9, no. 3, pp. 903-928, 2011.
- A. El Badia, T. Ha-Duong and A. Hamdi, “Identification of a point source in a linear advection–dispersion–reaction equation: application to a pollution source problem,” Inverse Problems, vol. 21, no. 3, pp. 1121, 2005.
- O. Khatib, “Real-time obstacle avoidance for manipulators and mobile robots,” Autonomous Robot Vehicles, Springer, 1986, pp. 396-404.
- T. Li, B. Jayawardhana, A. M. Kamat and A. G. P. Kottapalli, “Source-Seeking Control of Unicycle Robots With 3-D-Printed Flexible Piezoresistive Sensors,” IEEE Transactions on Robotics, vol. 38, no. 1, pp. 448-462, 2022.
- M.Z. Romdlony and B. Jayawardhana, “Stabilization with guaranteed safety using Control Lyapunov–Barrier Function,” Automatica, 66, pp. 39-47, 2016.
- M.Z. Romdlony and B. Jayawardhana, “On the new notion of Input-to-State Safety,” Proc. 55th IEEE Conference on Decision and Control, pp. 6403-6409, Las Vegas, 2016.
- M.Z. Romdlony and B. Jayawardhana, “Robustness analysis of systems’ safety through a new notion of input-to-state safety,” International Journal of Robust and Nonlinear Control, 29(7), pp. 2125-2136, 2019.
- D. Fox, W. Burgard, and S. Thrun, “The dynamic window approach to collision avoidance,” IEEE Robotics & Automation Magazine, vol. 4, no. 1, pp. 23-33, 1997.
- P. Ogren and N.Leonard, “A convergent dynamic window approach to obstacle avoidance,” IEEE Transactions on Robotics, vol. 21, no. 2, pp. 188-195, 2005.
- S. Prajna, “Barrier certificates for nonlinear model validation,” Automatica, vol. 42, no. 1, pp. 117-126, 2006.
- P. Wieland and F. Allgöwer, “ Constructive safety using control barrier functions,” IFAC Proceedings Volumes, vol. 40, no. 12, pp. 462-467, 2007.
- W. Xiao, C. Belta and C.G. Cassandras, “Adaptive control barrier functions,” IEEE Transactions on Automatic Control, vol. 67, no. 5, pp. 2267-2281, 2021.
- A.D. Ames, J.W. Grizzle, and P. Tabuada, “Control barrier function based quadratic programs with application to adaptive cruise control,” Proc. 53rd IEEE Conference on Decision and Control, December. 2014, pp. 6271-6278.
- A.D. Ames, X. Xu, J.W. Grizzle and P. Tabuada, “Control barrier function based quadratic programs for safety critical systems,” IEEE Transactions on Automatic Control, vol. 62, no. 8, pp. 3861-3876, 2016.
- A.D. Ames, S. Coogan, M. Egerstedt, G. Notomista, K.Sreenath, and P.Tabuada, “Control barrier functions: Theory and applications.” 2019 18th European control conference (ECC), 2019, pp. 3420-3431.
- H. Kong, F. He, X. Song, W. Hung and M. Gu, “Exponential-condition-based barrier certificate generation for safety verification of hybrid systems,” International Conference on Computer Aided Verification, 2013, pp. 242-257.
- L. Dai, T. Gan, B. Xia, and N. Zhan, “Barrier certificates revisited.” Journal of Symbolic Computation, vol. 80, pp. 62-86, 2017.
- Q. Nguyen and K. Sreenath, July, “Exponential control barrier functions for enforcing high relative-degree safety-critical constraints,” Proc. American Control Conference (ACC), July. 2016, pp. 322-328.
- Q. Nguyen and K. Sreenath, “ Robust safety-critical control for dynamic robotics,” IEEE Transactions on Automatic Control, vol. 67, no. 3, pp. 1073-1088, 2021.
- S. Boyd, S. P. Boyd, and L. Vandenberghe, “Convex optimization,” Cambridge university press, 2004, Chapter 5, pp. 243.
- X. Xu, P. Tabuada, J. W. Grizzle, and A.D. Ames, “Robustness of control barrier functions for safety critical control,” IFAC-PapersOnLine, vol. 48, no. 27, pp. 54-61, 2015.
- Y. Chen, A. Singletary and A. D. Ames,“Guaranteed obstacle avoidance for multi-robot operations with limited actuation: a control barrier function approach,” IEEE Control Systems Letters, vol. 5, no. 1, pp. 127-132, 2021.
- J. Fu, G.Wen, X. Yu and Z. Wu, “Distributed formation navigation of constrained second-order multiagent systems with collision avoidance and connectivity maintenance,” IEEE Transactions on Cybernetics, 2020.
- P. Glotfelter, J. Cortés and M. Egerstedt, “Nonsmooth barrier functions with applications to multi-robot systems,” IEEE control systems letters, vol. 1, no. 2, pp. 310-315, 2017.
- A. Singletary, A. Swann, Y. Chen and A. D. Ames, “Onboard Safety Guarantees for Racing Drones: High-Speed Geofencing With Control Barrier Functions,” IEEE Robotics and Automation Letters, vol. 7, no. 2, pp. 2897-2904, 2022.
- U. Borrmann, W. Li, A. D. Ames and M. Egerstedt, “Control barrier certificates for safe swarm behavior,” IFAC-PapersOnLine, vol. 48, no. 27, pp. 68-73, 2015.
- S. Hsu, X. Xu, and A. D. Ames, “Control barrier function based quadratic programs with application to bipedal robotic walking,” American Control Conference (ACC), 2015, pp. 4542-4548.
- Y. Chen, H. Peng, and J. Grizzle, “Obstacle avoidance for low-speed autonomous vehicles with barrier function,” IEEE Transactions on Control Systems Technology, vol. 26, no. 1, pp. 194-206, 2017.
- A. Manjunath and Q. Nguyen, “Safe and robust motion planning for dynamic robotics via control barrier functions,” 2021 60th IEEE Conference on Decision and Control (CDC), 2021, pp. 2122-2128.
- P. Glotfelter, I. Buckley and M. Egerstedt, “Hybrid nonsmooth barrier functions with applications to provably safe and composable collision avoidance for robotic systems,” IEEE Robotics and Automation Letters, vol. 4, no. 2, pp. 1303-1310, 2019.
- K. Majd, S. Yaghoubi, T. Yamaguchi, B. Hoxha, D. Prokhorov and G. Fainekos, “Safe navigation in human occupied environments using sampling and control barrier functions,” 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2021, pp. 5794-5800.
- S. Yaghoubi, K. Majd, G. Fainekos, T. Yamaguchi, D. Prokhorov and B. Hoxha, “Risk-bounded control using stochastic barrier functions,” IEEE Control Systems Letters, vol. 5, no. 5, pp. 1831-1836, 2020.
- N. Malone, H. -T. Chiang, K. Lesser, M. Oishi and L. Tapia, “Hybrid Dynamic Moving Obstacle Avoidance Using a Stochastic Reachable Set-Based Potential Field,” IEEE Transactions on Robotics, vol. 33, no. 5, pp. 1124-1138, 2017.
- J. Frasch, A. Gray, M. Zanon, H. Ferreau, S. Sager, F. Borrelli and M. Diehl, “An auto-generated nonlinear MPC algorithm for real-time obstacle avoidance of ground vehicles,” 2013 European Control Conference (ECC), 2013, pp. 4136-4141.
- H. Guo, C. Shen, H. Zhang, H. Chen and R. Jia, “Simultaneous trajectory planning and tracking using an MPC method for cyber-physical systems: A case study of obstacle avoidance for an intelligent vehicle,” IEEE Transactions on Industrial Informatics, vol. 14, no. 9, pp. 4273-4283, 2018.
- H. K. Khalil, “Nonlinear systems; 3rd ed,” Upper Saddle River, NJ: Prentice-Hall, 2002, the book can be consulted by contacting: PH-AID: Wallet, Lione.
- A. Scheinker, “Bounded extremum seeking for angular velocity actuated control of nonholonomic unicycle,” Optimal Control Applications and Methods, vol.38, no. 4, pp. 575-585, 2017.
- T. Xu, et al, “Fast source seeking with obstacle avoidance via extremum seeking control,” in 13th Asian Control Conference (ASCC), IEEE, 2022, pp. 2097-2102.
- H. B. Dürr, et al, “Obstacle avoidance for an extremum seeking system using a navigation function,” in 2013 American Control Conference, IEEE, 2013, pp.4062-4067.