A Unified Fractal Impedance Control Framework

Physical human-robot interaction requires yielding transiently to contact yet recovering the commanded reference under sustained load. Finite-stiffness impedance control retains a static deflection there, while predictive alternatives typically optimize a nonlinear robot or impedance model online. Operational-space cancellation instead exposes a translational error double integrator with a fixed transition matrix and a configuration-scheduled input map, making interaction a predictive quantity rather than a property re-derived per configuration. We build on it a compact offset-free interaction-error MPC for torque-controlled manipulators: a force-domain random-walk state estimates persistent interaction and model error, and a 30-variable convex QP maps the correction through the current task inertia while constraining the applied joint torque. Conditional results establish impedance equivalence of the unconstrained passive feedback, offset-free regulation at feasible frozen configurations, and quadratic stabilizability of the scheduled backbone. In a 1kHz MuJoCo simulation of a 7-DOF Franka FR3, the estimator cuts steady-state error under a repeated 15N step from 2.77mm to 0.042mm when added to the otherwise identical 100Hz MPC. A stiffness-and-damping-calibrated impedance baseline attains 2.59mm but briefly saturates and needs 3.3x the peak positive joint power. Adding ideal measured-force cancellation to that baseline gives 1.39mm, so constant-load rejection is not unique to MPC; the sensorless controller still reaches 0.042mm in the moving task, a 65x reduction without force sensing and without the baseline's saturation or power cost. Demonstrated in simulation under a shared actuator budget, the contribution is an efficient operational-space realization complementing rather than replacing broader interaction-control architectures.

Safe physical human--robot interaction on floating-base robots requires interaction regulation under changing contact constraints. We develop a contact-consistent normalization in which the residual end-effector channel is represented as a linear double integrator in acceleration coordinates. Both discrete prediction matrices are independent of configuration and support mode; posture and contact enter only through task-inertia force recovery and constraints. The controller combines a constant-Hessian receding-horizon QP, an acceleration-disturbance observer, and a priority-consistent realization. Classical operational-space impedance is shown to be the unconstrained infinite-horizon limit. MuJoCo experiments on a 17-DOF biped and a Menagerie-derived Unitree G1 model evaluate sustained forces, transmitted shocks, and scheduled contact-model changes. The observer sustains near-offset-free tracking across a genuine contact-set switch and a scheduled support-mode transition, while disturbance estimation---not contact consistency alone---is the dominant source of fixed-stance accuracy; covariance inflation gives only scenario-dependent transient benefit.

With advancements in learning-based policies, robots are increasingly being deployed in human-centric environments, such as manufacturing floors and homes, where safe and precise operation requires compensating for unknown loads while remaining compliant during human interactions. Reliably distinguishing between these interaction types is challenging with a single sensing modality, as force signals cannot separate payloads from human pushes, and vision is susceptible to occlusions. We propose a task-agnostic interaction estimation and adaptive control framework that addresses this challenge by fusing force history and 3D point cloud through a transformer-based classifier. Trained with modality dropout for occlusion resilience and fine-tuned from simulation to hardware, the classifier achieves 91.89% accuracy and maintains above 90% under complete occlusion of one modality. The classifier drives a system identification framework that selectively compensates for unknown payloads and a variable-impedance controller that switches between adaptive and reactive modes, while simultaneously estimating interaction forces for downstream tasks, such as human intent estimation. We validate the framework under external perturbations and unknown loads across single-arm manipulation, deployment with an imitation-learning-based policy, intent-driven target switching, and zero-shot bimanual deployment on two Franka arms lifting a box of unknown mass, demonstrating generalization to closed kinematic chains and unseen setups, enabling safe and precise deployment.