Numerical Methods for Reachable Space Generation of Humanoid Robots

In view of the importance of workspace to robotic design, motion planning and control, we study humanoid reachable spaces. Due to the large number of degrees of freedom, the complexity and special characteristics of humanoid robots that conventional robots do not possess, it would be very difficult or impractical to use analytical or geometric methods to analyze and obtain humanoid reachable spaces. In this paper, we develop two numerical approaches — the optimization-based method and the Monte Carlo method — to generate the reachable space of a humanoid robot. We first formulate the basic constraints (including kinematic constraint and balance constraint) that a humanoid robot must satisfy in manipulation tasks. We then use optimization techniques to build mathematical models for boundary points by which the reachable boundary is formed. This method gives rise to an approximation of the reachable space with accurate boundary points. On the other hand, the Monte Carlo method is relatively simple and more suitable for the visualization of robotic workspace. To utilize the numerical results by the Monte Carlo method, we propose an approach to build a database. We present the algorithms with these two methods and provide illustrating examples conducted on the humanoid HRP-2.