A branch-and-prune method to solve closure equations in dual quaternions

Using dual quaternions, the closure equations of a kinematic loop can be expressed as system multiaffine equations. In this paper, property is leveraged to introduce branch-and-prune method specially tailored for solving such systems The new objectively simpler (in sense that it easier understand and implement) than previous approaches relying on general techniques interval Newton methods or based Bernstein polynomials linear relaxations. Moreover, relies two basic operations — interpolation projection onto coordinate planes— efficiently computed. generality proposed evaluated position analysis problems with 0-, 1-, 2-dimensional solution sets, including inverse kinematics serial robots forward parallel ones. results obtained these show efficiency compares favorably state-of-the-art alternatives.