Kinematic motion planning using geometric mechanics tends to prescribe a trajectory in a parameterization of a shape space and determine its displacement in a position space. Often this trajectory is called a gait. Previous works assumed that the shape space is Euclidean when often it is not, either because the robotic joints can spin around forever (i.e., has an 𝕊1 configuration space component, or its parameterization has an 𝕊1 dimension). Consider a shape space that is a torus; gaits that “wrap” around the full range of a shape variable and return to its starting configuration are valid gaits in the shape space yet appear as line segments in the parameterization. Since such a gait does not form a closed loop in the parameterization, existing geometric mechanics methods cannot properly consider them. By explicitly analyzing the topology of the underlying shape space, we derive geometric tools to consider systems with toroidal and cylindrical shape spaces.
- Dynamic Systems and Control Division
Geometric Motion Planning for Systems With Toroidal and Cylindrical Shape Spaces
- Views Icon Views
- Share Icon Share
- Search Site
Gong, C, Ren, Z, Whitman, J, Grover, J, Chong, B, & Choset, H. "Geometric Motion Planning for Systems With Toroidal and Cylindrical Shape Spaces." Proceedings of the ASME 2018 Dynamic Systems and Control Conference. Volume 3: Modeling and Validation; Multi-Agent and Networked Systems; Path Planning and Motion Control; Tracking Control Systems; Unmanned Aerial Vehicles (UAVs) and Application; Unmanned Ground and Aerial Vehicles; Vibration in Mechanical Systems; Vibrations and Control of Systems; Vibrations: Modeling, Analysis, and Control. Atlanta, Georgia, USA. September 30–October 3, 2018. V003T32A013. ASME. https://doi.org/10.1115/DSCC2018-9144
Download citation file: