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.

Impedance MPC with Disturbance Estimation for Dexterous Hand Control

Dexterous hands must simultaneously track precise finger trajectories and maintain safe, compliant contact -- objectives in tension for any fixed-gain controller. We present an actuator-agnostic Impedance Model Predictive Control (Impedance MPC) framework for dexterous fingers, instantiating the constant-$A_d$ offset-free architecture established for physical human-robot interaction (pHRI); its stability, recursive-feasibility, and input-to-state-stability guarantees are inherited by preserving the architectural assumptions. An algebraic feedforward reduces the tendon transmission -- hydraulic, cable, pneumatic, twisted-string, or series-elastic -- to a constant-coefficient double integrator, so the QP cost inverse is precomputed offline and a 10-step receding-horizon quadratic program runs at 500\,Hz while enforcing hard constraints on contact force (ISO/TS 15066), actuation limits, and jerk. An encoder-only augmented-Kalman disturbance state drives steady-state error to zero under any constant contact load. On a hydraulically actuated finger -- the worked example platform, adding pressure and cavitation constraints -- the 500\,Hz Kalman MPC attains 0.5\,mrad RMS, 0.1\,mrad steady-state, and 6.6\,mrad peak deflection under 1.5\,Nm contact: 183$\times$, 1500$\times$, and 23$\times$ better than classical impedance. The realized first-move stiffness (18$\to$323\,Nm/rad with update rate) is independently verified. The architecture scales to a 16-DOF LEAP Hand MuJoCo simulation, recovering from 2.5\,N grasp-load disturbances within 0.7\,s.

Impedance MPC with Patient-Torque Estimation for Knee Rehabilitation Exoskeletons

Knee rehabilitation exoskeletons must enforce a prescribed joint trajectory while remaining safely compliant with involuntary spasm and voluntary patient effort-objectives in tension for any fixed-gain impedance controller. We present an Impedance Model Predictive Control framework for knee rehabilitation exoskeletons, demonstrated on a series-elastic-actuator (SEA) platform: an algebraic feedforward reduces the knee dynamics to a constant-coefficient scalar double integrator, and a receding-horizon quadratic program (QP) computes corrective torques while enforcing hard range-of-motion, torque, and velocity limits (ISO 13482). A Kalman disturbance state driven by direct SEA-based torque sensing (the series-elastic spring deflection measured through the elastic element - an intrinsic, EMG-free patient-torque estimate, not a separate load cell) gives a nominal offset-free guarantee and, via its sign and the desired-motion direction, sensorless Assist-as-Needed. The constant state matrix permits offline precomputation of the QP cost inverse, enabling 500 Hz operation with a multi-step horizon. Across seven-controller benchmarks (sinusoidal tracking, isometric hold), the 500 Hz Kalman MPC is offset free 0.1 mrad RMS, 0.1 mrad steady-state, 0.2 mrad peak under 15 Nm spasm, versus a 515 mrad steady-state offset for classical impedance at the same stiffness - the direct-measurement channel converging the estimate near-immediately (within a few sampling periods). Without the estimator it realizes a classical impedance (4.8 mrad RMS, 8.3 mrad steady-state). All MPC variants meet the 87 mrad clinical criterion; no classical controller does. The architecture is formulated for the 20 DOF MyoSuite myoLeg via coupling-aware per-joint QPs.

Impedance MPC for Physical Human-Robot Interaction: Predictive Disturbance Rejection with Joint-Limit Safety

Physical human-robot interaction (pHRI) demands simultaneous trajectory accuracy and compliant safety under unplanned contact. Classical impedance control incurs a nonzero steady-state position error under sustained human force -- the applied force divided by the task stiffness -- which integral action reduces only within a narrow stable-gain budget. We present a two-layer Impedance MPC that resolves this tension. Layer~1 analytically cancels gravity, Coriolis, and task-space inertia, reducing the residual plant to a configuration-independent double integrator with a constant state-transition matrix. Layer~2 solves a 30-variable convex QP at 100\,Hz, exploiting this constant structure so the free-response matrix is precomputed once; an augmented Kalman filter estimates the persistent disturbance state, giving a formal zero-steady-state-error guarantee. A null-space inverse-barrier potential and a task-space workspace projection enforce joint-limit safety across the tested workspace. On a 7-DOF Franka FR3, Impedance MPC with Kalman augmentation attains sub-0.05\,mm steady-state error versus 44.8\,mm for classical impedance (a $>$800-fold reduction) under a sustained 15\,N force, sub-millimeter tracking on four 3-D circles, and graceful robustness to measurement noise and inertial mismatch up to 30\%.