Servos for Local Map Exploration Onboard Nonholonomic Vehicles for Extremum Seeking
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914048518389760 |
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| author | James-Kavanaugh, Dylan McNamee, Patrick Wang, Qixu Ahmadabadi, Zahra Nili |
| author_facet | James-Kavanaugh, Dylan McNamee, Patrick Wang, Qixu Ahmadabadi, Zahra Nili |
| contents | Extremum seeking control (ESC) often employs perturbation-based estimates of derivatives for some sensor field or cost function. These estimates are generally obtained by simply multiplying the output of a single-unit sensor by some time-varying function. Previous work has focused on sinusoidal perturbations to generate derivative estimates with results for arbitrary order derivatives of scalar maps or higher up to third-order derivatives of multivariable maps. This work extends the perturbations from sinusoidal to bounded periodic or almost periodic functions and considers multivariable maps. A necessary and sufficient condition is given for determining if time-varying functions exist for estimating arbitrary order derivatives of multivariable maps for any given bounded periodic or almost periodic dither signal. These results are then used in a source seeking controller for a nonholonomic vehicle with a sensor actuated by servo. The conducted simulation and real-world experiments demonstrate that by distributing the local map exploration to a servo, the nonholonomic vehicle was able to achieve a faster convergence to the source. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_16365 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Servos for Local Map Exploration Onboard Nonholonomic Vehicles for Extremum Seeking James-Kavanaugh, Dylan McNamee, Patrick Wang, Qixu Ahmadabadi, Zahra Nili Systems and Control Robotics Extremum seeking control (ESC) often employs perturbation-based estimates of derivatives for some sensor field or cost function. These estimates are generally obtained by simply multiplying the output of a single-unit sensor by some time-varying function. Previous work has focused on sinusoidal perturbations to generate derivative estimates with results for arbitrary order derivatives of scalar maps or higher up to third-order derivatives of multivariable maps. This work extends the perturbations from sinusoidal to bounded periodic or almost periodic functions and considers multivariable maps. A necessary and sufficient condition is given for determining if time-varying functions exist for estimating arbitrary order derivatives of multivariable maps for any given bounded periodic or almost periodic dither signal. These results are then used in a source seeking controller for a nonholonomic vehicle with a sensor actuated by servo. The conducted simulation and real-world experiments demonstrate that by distributing the local map exploration to a servo, the nonholonomic vehicle was able to achieve a faster convergence to the source. |
| title | Servos for Local Map Exploration Onboard Nonholonomic Vehicles for Extremum Seeking |
| topic | Systems and Control Robotics |
| url | https://arxiv.org/abs/2509.16365 |