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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.01153 |
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| _version_ | 1866910469455872000 |
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| author | Liu, Zhi Wu, Si Liu, Tengfei Jiang, Zhong-Ping |
| author_facet | Liu, Zhi Wu, Si Liu, Tengfei Jiang, Zhong-Ping |
| contents | This paper studies the safety-critical control problem for Euler-Lagrange (EL) systems subject to multiple ball obstacles and velocity constraints in accordance with affordable velocity ranges. A key strategy is to exploit the underlying inner-outer-loop structure for the design of a new cascade controller for the class of EL systems. In particular, the outer-loop controller is developed based on quadratic programming (QP) to avoid ball obstacles and generate velocity reference signals fulfilling the velocity limitation. Taking full advantage of the conservation-of-energy property, a nonlinear velocity-tracking controller is designed to form the inner loop. One major difficulty is caused by the possible non-Lipschitz continuity of the standard QP algorithm when there are multiple constraints. To solve this problem, we propose a refined QP algorithm with the feasible set reshaped by an appropriately chosen positive basis such that the feasibility is retained while the resulting outer-loop controller is locally Lipschitz. It is proved that the constraint-satisfaction problem is solvable as long as the ball obstacles satisfy a mild distance condition. The proposed design is validated by numerical simulation and an experiment based on a $2$-link planar manipulator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01153 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Safety-Critical Control of Euler-Lagrange Systems Subject to Multiple Obstacles and Velocity Constraints Liu, Zhi Wu, Si Liu, Tengfei Jiang, Zhong-Ping Systems and Control This paper studies the safety-critical control problem for Euler-Lagrange (EL) systems subject to multiple ball obstacles and velocity constraints in accordance with affordable velocity ranges. A key strategy is to exploit the underlying inner-outer-loop structure for the design of a new cascade controller for the class of EL systems. In particular, the outer-loop controller is developed based on quadratic programming (QP) to avoid ball obstacles and generate velocity reference signals fulfilling the velocity limitation. Taking full advantage of the conservation-of-energy property, a nonlinear velocity-tracking controller is designed to form the inner loop. One major difficulty is caused by the possible non-Lipschitz continuity of the standard QP algorithm when there are multiple constraints. To solve this problem, we propose a refined QP algorithm with the feasible set reshaped by an appropriately chosen positive basis such that the feasibility is retained while the resulting outer-loop controller is locally Lipschitz. It is proved that the constraint-satisfaction problem is solvable as long as the ball obstacles satisfy a mild distance condition. The proposed design is validated by numerical simulation and an experiment based on a $2$-link planar manipulator. |
| title | Safety-Critical Control of Euler-Lagrange Systems Subject to Multiple Obstacles and Velocity Constraints |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2406.01153 |