Singularity-Robust Prioritized Whole-Body Tracking and Interaction Control with Smooth Task Transitions

In this work, we propose a singularity-robust whole-body control framework that ensures smooth task tran- sitions while maintaining strict priorities. The weighted gener- alized inverse is adopted to derive a hierarchical control law compatible with singular and redundant tasks. Moreover, a smooth activation matrix is proposed to continuously shape both null-space projectors and task-level control actions. Vali- dation has been conducted in MATLAB/Simulink and MuJoCo simulations with Rollin’ Justin.