Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.07983 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908461657227264 |
|---|---|
| author | Surov, Maksim |
| author_facet | Surov, Maksim |
| contents | This paper addresses the feasibility of virtual holonomic constraints (VHCs) in the context of motion planning for underactuated mechanical systems with a single degree of underactuation. While existing literature has established a widely accepted definition of VHC, we argue that this definition is overly restrictive and excludes a broad class of admissible trajectories from consideration. To illustrate this point, we analyze a periodic motion of the Planar Vertical Take-Off and Landing (PVTOL) aircraft that satisfies all standard motion planning requirements, including orbital stabilizability. However, for this solution -- as well as for a broad class of similar ones -- there exists no VHC that satisfies the conventional definition. We further provide a formal proof demonstrating that the conditions imposed by this definition necessarily fail for a broad class of trajectories of mechanical systems. These findings call for a reconsideration of the current definition of VHCs, with the potential to significantly broaden their applicability in motion planning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07983 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Virtual Holonomic Constraints in Motion Planning: Revisiting Feasibility and Limitations Surov, Maksim Robotics This paper addresses the feasibility of virtual holonomic constraints (VHCs) in the context of motion planning for underactuated mechanical systems with a single degree of underactuation. While existing literature has established a widely accepted definition of VHC, we argue that this definition is overly restrictive and excludes a broad class of admissible trajectories from consideration. To illustrate this point, we analyze a periodic motion of the Planar Vertical Take-Off and Landing (PVTOL) aircraft that satisfies all standard motion planning requirements, including orbital stabilizability. However, for this solution -- as well as for a broad class of similar ones -- there exists no VHC that satisfies the conventional definition. We further provide a formal proof demonstrating that the conditions imposed by this definition necessarily fail for a broad class of trajectories of mechanical systems. These findings call for a reconsideration of the current definition of VHCs, with the potential to significantly broaden their applicability in motion planning. |
| title | Virtual Holonomic Constraints in Motion Planning: Revisiting Feasibility and Limitations |
| topic | Robotics |
| url | https://arxiv.org/abs/2505.07983 |