A singularity-tolerant inverse kinematics including joint position and velocity limitations

Humanoid robots have many degrees of freedom which ideally enables them to accomplish different tasks. From a control viewpoint, however, the geometric complexity makes planning and control difficult. Favoring controllability properties, it is popular to operate with crouched knees, since the Center of Mass (CoM) height can be directly manipulated. In addition to a higher energy consumption however, this brings long-term damage to the actuator and series elastic elements. We propose a simple Inverse Kinematics (IK) formulation as a nonlinear optimization that can handle singularities and joint limits with inequality constraints. We also introduce safe regions for joint velocities and propose modifications that help the joint come out of singularities faster. The effectiveness of the proposed method is verified in simulations and on the real hardware for various balancing tasks