Integrator Forwading Design for Unicycles with Constant and Actuated Velocity in Polar Coordinates
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915524065099776 |
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| author | Krstic, Miroslav Todorovski, Velimir Kim, Kwang Hak Astolfi, Alessandro |
| author_facet | Krstic, Miroslav Todorovski, Velimir Kim, Kwang Hak Astolfi, Alessandro |
| contents | In a companion paper, we present a modular framework for unicycle stabilization in polar coordinates that provides smooth steering laws through backstepping. Surprisingly, the same problem also allows the application of integrator forwarding. In this work, we leverage this feature and construct new smooth steering laws together with control Lyapunov functions (CLFs), expanding the set of CLFs available for inverse optimal control design. In the case of constant forward velocity (Dubins car), backstepping produces finite-time (deadbeat) parking, and we show that integrator forwarding yields the very same class of solutions. This reveals a fundamental connection between backstepping and forwarding in addressing both the unicycle and, the Dubins car parking problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25579 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integrator Forwading Design for Unicycles with Constant and Actuated Velocity in Polar Coordinates Krstic, Miroslav Todorovski, Velimir Kim, Kwang Hak Astolfi, Alessandro Systems and Control Robotics Optimization and Control In a companion paper, we present a modular framework for unicycle stabilization in polar coordinates that provides smooth steering laws through backstepping. Surprisingly, the same problem also allows the application of integrator forwarding. In this work, we leverage this feature and construct new smooth steering laws together with control Lyapunov functions (CLFs), expanding the set of CLFs available for inverse optimal control design. In the case of constant forward velocity (Dubins car), backstepping produces finite-time (deadbeat) parking, and we show that integrator forwarding yields the very same class of solutions. This reveals a fundamental connection between backstepping and forwarding in addressing both the unicycle and, the Dubins car parking problems. |
| title | Integrator Forwading Design for Unicycles with Constant and Actuated Velocity in Polar Coordinates |
| topic | Systems and Control Robotics Optimization and Control |
| url | https://arxiv.org/abs/2509.25579 |