Whole-Body Impedance Model Predictive Control for Safe Physical Human--Robot Interaction on Floating-Base Platforms

Floating-base robots must balance under rigid contact constraints while interacting safely with humans. Existing whole-body control~(WBC) frameworks allocate the full joint space to locomotion or rely on fixed-gain impedance feedback that accumulates steady-state error under sustained physical human--robot interaction~(pHRI) forces. This paper extends the authors' fixed-base two-layer Impedance MPC to floating-base platforms through a three-level architecture: a centroidal MPC plans contact forces over a 500\,ms horizon; a priority-driven WBC layer resolves balance into joint torques through contact-consistent null-space projection; and the residual null space is governed by a receding-horizon quadratic program~(QP) that predicts and rejects pHRI disturbances using a Kalman-augmented state. A contact-consistent feedback linearization reduces the arm end-effector plant to a double integrator with a \emph{constant} state matrix within each contact mode, enabling offline precomputation of the QP cost and ${\geq}1$\,kHz operation. A covariance-inflation protocol preserves the disturbance estimate across contact-mode switches, guaranteeing zero steady-state error under bounded constant pHRI loads, and an Impedance Equivalence Theorem shows the infinite-horizon limit recovers a classical task-space impedance law whose effective mass, damping, and stiffness adapt to posture and contact configuration. Simulations on a 17-DOF biped and the Unitree G1 humanoid validate the design.