Trajectory Planning with Signal Temporal Logic Costs using Deterministic Path Integral Optimization
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913716186906624 |
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| author | Halder, Patrick Homburger, Hannes Kiltz, Lothar Reuter, Johannes Althoff, Matthias |
| author_facet | Halder, Patrick Homburger, Hannes Kiltz, Lothar Reuter, Johannes Althoff, Matthias |
| contents | Formulating the intended behavior of a dynamic system can be challenging. Signal temporal logic (STL) is frequently used for this purpose due to its suitability in formalizing comprehensible, modular, and versatile spatiotemporal specifications. Due to scaling issues with respect to the complexity of the specifications and the potential occurrence of non-differentiable terms, classical optimization methods often solve STL-based problems inefficiently. Smoothing and approximation techniques can alleviate these issues but require changing the optimization problem. This paper proposes a novel sampling-based method based on model predictive path integral control to solve optimal control problems with STL cost functions. We demonstrate the effectiveness of our method on benchmark motion planning problems and compare its performance with state-of-the-art methods. The results show that our method efficiently solves optimal control problems with STL costs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_01476 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trajectory Planning with Signal Temporal Logic Costs using Deterministic Path Integral Optimization Halder, Patrick Homburger, Hannes Kiltz, Lothar Reuter, Johannes Althoff, Matthias Systems and Control Robotics Formulating the intended behavior of a dynamic system can be challenging. Signal temporal logic (STL) is frequently used for this purpose due to its suitability in formalizing comprehensible, modular, and versatile spatiotemporal specifications. Due to scaling issues with respect to the complexity of the specifications and the potential occurrence of non-differentiable terms, classical optimization methods often solve STL-based problems inefficiently. Smoothing and approximation techniques can alleviate these issues but require changing the optimization problem. This paper proposes a novel sampling-based method based on model predictive path integral control to solve optimal control problems with STL cost functions. We demonstrate the effectiveness of our method on benchmark motion planning problems and compare its performance with state-of-the-art methods. The results show that our method efficiently solves optimal control problems with STL costs. |
| title | Trajectory Planning with Signal Temporal Logic Costs using Deterministic Path Integral Optimization |
| topic | Systems and Control Robotics |
| url | https://arxiv.org/abs/2503.01476 |