Hybrid Feedback Control for Global and Optimal Safe Navigation (2402.17038v2)
Abstract: We propose a hybrid feedback control strategy that safely steers a point-mass robot to a target location optimally from all initial conditions in the n-dimensional Euclidean space with a single spherical obstacle. The robot moves straight to the target when it has a clear line-of-sight to the target location. Otherwise, it engages in an optimal obstacle avoidance maneuver via the shortest path inside the cone enclosing the obstacle and having the robot's position as a vertex. The switching strategy that avoids the undesired equilibria, leading to global asymptotic stability (GAS) of the target location, relies on using two appropriately designed virtual destinations, ensuring control continuity and shortest path generation. Simulation results illustrating the effectiveness of the proposed approach are presented.
- O. Khatib, “Real time obstacle avoidance for manipulators and mobile robots,” The International Journal of Robotics Research, vol. 5, no. 1, pp. 90–99, 1986.
- D. E. Koditchek and E. D. Rimon, “Robot Navigation Functions on Manifolds with Boundary,” ADVANCES IN APPLIED MATHEMATICS, vol. 11, pp. 412–442, 1990.
- E. D. Rimon and D. E. Koditchek, “Exact Robot Navigation Using Artificial Potential Functions,” IEEE Transactions on Robotics and Automation, vol. 8, no. 5, pp. 501–518, 1992.
- S. G. Loizou, “The navigation transformation,” IEEE Transactions on Robotics, vol. 33, no. 6, pp. 1516–1523, 2017.
- N. Constantinou and S. G. Loizou, “Robot navigation on star worlds using a single-step navigation transformation,” in 2020 59th IEEE Conference on Decision and Control (CDC), pp. 1537–1542, 2020.
- S. Paternain, D. E. Koditschek, and A. Ribeiro, “Navigation functions for convex potentials in a space with convex obstacles,” IEEE Transactions on Automatic Control, vol. 63, no. 9, pp. 2944–2959, 2018.
- O. Arslan and D. E. Koditschek, “Sensor-based reactive navigation in unknown convex sphere worlds,” The International Journal of Robotics Research, vol. 38, no. 2-3, pp. 196–223, 2019.
- V. G. Vasilopoulos and D. E. Koditschek, “Reactive Navigation in Partially Known Non-Convex Environments,” in 13th International Workshop on the Algorithmic Foundations of Robotics (WAFR), 2018.
- V. G. Vasilopoulos, G. Pavlakos, K. Schmeckpeper, K. Daniilidis, and D. E. Koditschek, “Reactive navigation in partially familiar planar environments using semantic perceptual feedback,” ArXiv, vol. abs/2002.08946, 2020.
- I. Cheniouni, A. Tayebi, and S. Berkane, “Safe and quasi-optimal autonomous navigation in sphere worlds,” in 2023 American Control Conference (ACC), pp. 2678–2683, 2023.
- I. Cheniouni, S. Berkane, and A. Tayebi, “Safe and quasi-optimal autonomous navigation in environments with convex obstacles,” arXiv:2308.13425, 2023.
- S. Berkane, A. Bisoffi, and D. V. Dimarogonas, “A hybrid controller for obstacle avoidance in an n𝑛nitalic_n-dimensional euclidean space,” in 2019 18th European Control Conference (ECC), pp. 764–769, 2019.
- S. Berkane, A. Bisoffi, and D. V. Dimarogonas, “Obstacle avoidance via hybrid feedback,” IEEE Transactions on Automatic Control, vol. 67, no. 1, pp. 512–519, 2022.
- M. Sawant, S. Berkane, I. Polushin, and A. Tayebi, “Hybrid feedback for autonomous navigation in planar environments with convex obstacles,” IEEE Transactions on Automatic Control, pp. 1–16, 2023.
- M. Sawant, A. Tayebi, and I. Polushin, “Hybrid feedback control design for non-convex obstacle avoidance,” arXiv:2304.10598, 2023.
- C. D. Meyer, Matrix Analysis and Applied Linear Algebra. USA: Society for Industrial and Applied Mathematics, 2000.
- Princeton University Press, 2012.
- S. Berkane and A. Tayebi, “On the design of attitude complementary filters on so(3)𝑠𝑜3so(3)italic_s italic_o ( 3 ),” IEEE Transactions on Automatic Control, vol. 63, no. 3, pp. 880–887, 2017.
- J. Chai and R. G. Sanfelice, “Forward invariance of sets for hybrid dynamical systems (part i),” IEEE Transactions on Automatic Control, vol. 64, no. 6, pp. 2426–2441, 2019.