PV-OSIMr: A Lowest Order Complexity Algorithm for Computing the Delassus Matrix
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| Format: | Preprint |
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2023
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| _version_ | 1866917736940044288 |
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| author | Sathya, Ajay Suresha Decre, Wilm Swevers, Jan |
| author_facet | Sathya, Ajay Suresha Decre, Wilm Swevers, Jan |
| contents | We present PV-OSIMr, an efficient algorithm for computing the Delassus matrix (also known as the inverse operational space inertia matrix) for a kinematic tree, with the lowest order computational complexity known in literature. PV-OSIMr is derived by optimizing the Popov-Vereshchagin (PV) solver computations using the compositionality of the force and motion propagators. It has a computational complexity of O(n + m^2 ) compared to O(n + m^2d) of the original PV-OSIM algorithm and O(n+md+m^2 ) of the extended force propagator algorithm (EFPA), where n is the number of joints, m is the number of constraints and d is the depth of the kinematic tree. Since Delassus matrix computation requires constructing an m x m sized matrix and must consider all the n joints at least once, the asymptotic computational complexity of PV-OSIMr is optimal. We further benchmark our algorithm and find it to be often more efficient than the PV-OSIM and EFPA in practice. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_03676 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | PV-OSIMr: A Lowest Order Complexity Algorithm for Computing the Delassus Matrix Sathya, Ajay Suresha Decre, Wilm Swevers, Jan Robotics We present PV-OSIMr, an efficient algorithm for computing the Delassus matrix (also known as the inverse operational space inertia matrix) for a kinematic tree, with the lowest order computational complexity known in literature. PV-OSIMr is derived by optimizing the Popov-Vereshchagin (PV) solver computations using the compositionality of the force and motion propagators. It has a computational complexity of O(n + m^2 ) compared to O(n + m^2d) of the original PV-OSIM algorithm and O(n+md+m^2 ) of the extended force propagator algorithm (EFPA), where n is the number of joints, m is the number of constraints and d is the depth of the kinematic tree. Since Delassus matrix computation requires constructing an m x m sized matrix and must consider all the n joints at least once, the asymptotic computational complexity of PV-OSIMr is optimal. We further benchmark our algorithm and find it to be often more efficient than the PV-OSIM and EFPA in practice. |
| title | PV-OSIMr: A Lowest Order Complexity Algorithm for Computing the Delassus Matrix |
| topic | Robotics |
| url | https://arxiv.org/abs/2310.03676 |