Stratified Deformation Space and Path Planning for a Planar Closed Chain with Revolute Joints [chapter]

L. Han, L. Rudolph, J. Blumenthal, I. Valodzin
Springer Tracts in Advanced Robotics  
Given a linkage belonging to any of several broad classes (both planar and spatial), we have defined parameters adapted to a stratification of its deformation space (the quotient space of its configuration space by the group of rigid motions) making that space "practically piecewise convex". This leads to great simplifications in motion planning for the linkage, because in our new parameters the loop closure constraints are exactly, not approximately, a set of linear inequalities. We illustrate
more » ... the general construction in the case of planar nR loops (closed chains with revolute joints), where the deformation space (link collisions allowed) has one connected component or two, stratified by copies of a single convex polyhedron via proper boundary identification. In essence, our approach makes path planning for a planar nR loop essentially no more difficult than for an open chain. The authors acknowledge computing support from NSF award DBI-0320875, and thank the anonymous reviewers for their helpful comments.
doi:10.1007/978-3-540-68405-3_15 fatcat:q7ci2tkdbjhetilxbly6cxakwm