Reachable boundary of a humanoid robot with two feet fixed on the ground

For planning and implementation of manipulation tasks using one or two arms/hands of a humanoid robot, which would be the most common application of the robot in the future, it is undoubtedly important to know the workspace of the robot. In this paper, we study the reachable space or boundary of an arm/hand when the humanoid robot stands on the ground with its two feet fixed. Since a humanoid robot has more degrees of freedom than a traditional robot and special characters that the latter does not possess, it would be very difficult or impractical to use conventional methods to analyze and obtain its reachable space. Here we propose a numerical approach to analyze and generate humanoid reachable space. Taking into account the robot balance, the geometric and kinematic constraints, we use optimization technique to build mathematic models for the reachable boundary. This discrete method gives rise to an approximation of the reachable space though, it is adequate for practical application. The proposed algorithm is illustrated by an example conducted on the humanoid platform HRP-2, and can be extended to more complex cases