Motion planning for humanoid robot anticipating environmental changes

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We have developed a new motion planning framework using the mathematical concept of a quotient-space, through removal of a dimension to improve the efficiency of computation. A quotient-space is a simplified space, which is created by declaring points in a space as being equivalent, and then grouping them together into a single point of the quotient-space. We realized this simplification through the idea of nesting robots in each other.Our approach is general to be applied to any robot. Fo a manipulator arm, we nest a series of lower-dimensional manipulator arms inside the original arm, whereby each lower-dimensional arm is created by removing a link of the arm. This nesting of robots creates a series of quotient-spaces, which are all nested inside the original configuration space.We have subsequently developed a new algorithm, called the quotient-space roadmap planner (QMP), which is able to exploit quotient-spaces. Our planner is unique in that it uses simplifications while being complete. Being complete means that we will find a path for a planning problem, whenever one exists.Our algorithm QMP works by first decomposing the configuration into its quotient-spaces. Then we start growing a graph on the lowest-dimensional quotient-space until we find a feasible path. Once such a path has been found, we start growing a second graph on the next quotient-space. Both graphs are simultaneously grown until a feasible path is found on the next quotient-space. This process is continued until we find a path on the configuration space itself.