Since the constraints are expressed with polynomials, it may not be
surprising that the computational algebraic geometry methods of
Section 6.4 can solve the general motion planning problem
with closed kinematic chains. Either cylindrical algebraic
decomposition or Canny's roadmap algorithm may be applied. As
mentioned in Section 6.5.3, an adaptation of the roadmap
algorithm that is optimized for problems in which is given in
[76].

Steven M LaValle
2012-04-20