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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2406.16874 |
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| _version_ | 1866913417231597568 |
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| author | Rabiee, Pedram Hoagg, Jesse B. |
| author_facet | Rabiee, Pedram Hoagg, Jesse B. |
| contents | We present a closed-form optimal control that satisfies both safety constraints (i.e., state constraints) and input constraints (e.g., actuator limits) using a composition of multiple control barrier functions (CBFs). This main contribution is obtained through the combination of several ideas. First, we present a method for constructing a single relaxed control barrier function (R-CBF) from multiple CBFs, which can have different relative degrees. The construction relies on a log-sum-exponential soft-minimum function and yields an R-CBF whose zero-superlevel set is a subset of the intersection of the zero-superlevel sets of all CBFs used in the composition. Next, we use the soft-minimum R-CBF to construct a closed-form control that is optimal with respect to a quadratic cost subject to the safety constraints. Finally, we use the soft-minimum R-CBF to develop a closed-form optimal control that not only guarantees safety but also respects input constraints. The key elements in developing this novel control include: the introduction of the control dynamics, which allow the input constraints to be transformed into controller-state constraints; the use of the soft-minimum R-CBF to compose multiple safety and input CBFs, which have different relative degrees; and the development of a desired surrogate control (i.e., a desired input to the control dynamics). We demonstrate these new control approaches in simulation on a nonholonomic ground robot. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16874 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Closed-Form Control for Safety Under Input Constraints Using a Composition of Control Barrier Functions Rabiee, Pedram Hoagg, Jesse B. Systems and Control We present a closed-form optimal control that satisfies both safety constraints (i.e., state constraints) and input constraints (e.g., actuator limits) using a composition of multiple control barrier functions (CBFs). This main contribution is obtained through the combination of several ideas. First, we present a method for constructing a single relaxed control barrier function (R-CBF) from multiple CBFs, which can have different relative degrees. The construction relies on a log-sum-exponential soft-minimum function and yields an R-CBF whose zero-superlevel set is a subset of the intersection of the zero-superlevel sets of all CBFs used in the composition. Next, we use the soft-minimum R-CBF to construct a closed-form control that is optimal with respect to a quadratic cost subject to the safety constraints. Finally, we use the soft-minimum R-CBF to develop a closed-form optimal control that not only guarantees safety but also respects input constraints. The key elements in developing this novel control include: the introduction of the control dynamics, which allow the input constraints to be transformed into controller-state constraints; the use of the soft-minimum R-CBF to compose multiple safety and input CBFs, which have different relative degrees; and the development of a desired surrogate control (i.e., a desired input to the control dynamics). We demonstrate these new control approaches in simulation on a nonholonomic ground robot. |
| title | A Closed-Form Control for Safety Under Input Constraints Using a Composition of Control Barrier Functions |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2406.16874 |