Robotic manipulators and the geometry of real semialgebraic sets

Some modern techniques are applied from real semialgebraic geometry to the robotic manipulator problem. In particular, using the notion of "metric entropy," the complexity of maneuvering the manipulator from state to state is discussed.

[1]  François Treves,et al.  On the local solvability and the local integrability of systems of vector fields , 1983 .

[2]  M. Coste Ensembles semi-algebriques , 1982 .

[3]  G. Lorentz Metric entropy and approximation , 1966 .

[4]  H. Warren Lower bounds for approximation by nonlinear manifolds , 1968 .

[5]  K. H. Hunt,et al.  Kinematic geometry of mechanisms , 1978 .

[6]  Robert Hardt,et al.  Semi-Algebraic Local-Triviality in Semi-Algebraic Mappings , 1980 .

[7]  Yosef Yomdin,et al.  The geometry of critical and near-critical values of differentiable mappings , 1983 .

[8]  I. Shafarevich Basic algebraic geometry , 1974 .

[9]  Roger W. Brockett,et al.  Robotic manipulators and the product of exponentials formula , 1984 .

[10]  A. Tarski A Decision Method for Elementary Algebra and Geometry , 2023 .

[11]  J. Schwartz,et al.  On the “piano movers'” problem I. The case of a two‐dimensional rigid polygonal body moving amidst polygonal barriers , 1983 .

[12]  J. Schwartz,et al.  On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds , 1983 .

[13]  K. H. Hunt,et al.  Quadruple dwell from a four-bar spatial linkage , 1971 .

[14]  Joseph K. Davidson,et al.  The Dual Torus and Associated Linkages , 1983 .

[15]  Y. Yomdin GLOBAL BOUNDS FOR THE BETTI NUMBERS OF REGULAR FIBERS OF DIFFERENTIABLE MAPPINGS , 1985 .

[16]  R. Hardt Stratification of real analytic mappings and images , 1975 .