TY - GEN
T1 - Geometric motion planning for systems with toroidal and cylindrical shape spaces
AU - Gong, Chaohui
AU - Ren, Zhongqiang
AU - Whitman, Julian
AU - Grover, Jaskaran
AU - Chong, Baxi
AU - Choset, Howie
N1 - Publisher Copyright:
Copyright © 2018 ASME.
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/85057387495
UR - https://www.scopus.com/pages/publications/85057387495#tab=citedBy
U2 - 10.1115/DSCC2018-9144
DO - 10.1115/DSCC2018-9144
M3 - Conference contribution
AN - SCOPUS:85057387495
T3 - ASME 2018 Dynamic Systems and Control Conference, DSCC 2018
BT - 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
PB - American Society of Mechanical Engineers (ASME)
T2 - ASME 2018 Dynamic Systems and Control Conference, DSCC 2018
Y2 - 30 September 2018 through 3 October 2018
ER -