Robust Adaptive Backstepping Impedance Control of Robots in Unknown Environments

Safe physical interaction is critical for deploying robotic manipulators in human-robot interaction and contact-rich tasks, where uncertainty, external forces, and actuator limitations can compromise both performance and safety. We propose an online adaptive impedance control framework that enforces joint-state safety while achieving compliant interaction under uncertain dynamics. The approach combines a quadratic-program-based safety filter with a novel composed position-velocity non-smooth control barrier function (NCBF), enabling joint position and velocity constraints to be enforced through a unified relative-degree-one barrier. Unknown dynamics are compensated online using an interval type-2 fuzzy logic system, while actuator torque limits are handled through soft constraints with exact penalty recovery of feasible solutions. A disturbance-observer-enhanced safety mechanism improves robustness against modelling errors and external interaction forces. Using composite Lyapunov analysis, we prove forward invariance of the safe set and the uniform ultimately boundedness of the impedance-tracking error. Simulations on a 7-DOF manipulator with severe parametric uncertainty and external interaction wrenches demonstrate safe constraint satisfaction and robust impedance tracking.

Contact-rich manipulation requires robots to regulate force against surfaces whose geometry deviates unpredictably from training conditions. Trajectory-based imitation learning, which reproduces observable outputs, breaks down under such shifts. We propose Impedance Cloning, which instead imitates the biomechanical priors that generate motion -- the stiffness and equilibrium point -- and thereby passively absorbs contact uncertainty. Because these parameters encode intent rather than outcome, they generalize across surface geometries where trajectory reproduction does not. We extract them from bilateral teleoperation demonstrations via a particle filter without force/torque sensors and evaluate the framework on two CRANE-X7 manipulators. In a wiping task with joint-space actions, the trajectory-based baseline loses contact below -6 cm, whereas the proposed method maintains a consistent 4-5 N contact force above -6 cm, with a gradual decrease below; with Cartesian-space actions, its force-height slope over 0 to +8 cm is 0.13 +/- 0.03 N/cm, versus 0.34-0.83 N/cm for fixed-impedance baselines. In a pick-and-place task with 10 diverse cups (100 trials), the proposed method succeeds in 84 trials, outperforming the fixed-impedance baseline (74/100) and performing comparably to a variable impedance control baseline (82/100) with one demonstration instead of ten. In a grasping task, the representation reduces torque tracking error with both ILBiT and Mamba backbones, confirming its generality across architectures.

Learning-based manipulation policies usually predict robot actions from sensory observations and leave their execution to a separate low-level controller. In rigid contact, this separation can be problematic: the same motion to a virtual target or compliant motion command can lead to unstable contact, tracking error, excessive loading, or tool damage, depending on the low-level controller. In this paper, we propose a Unified Robot Control-Policy Framework (URF), which connects compliant action prediction with unified impedance-admittance control. Given multimodal observations, URF predicts a virtual target, a stiffness matrix, and an impedance-admittance switch ratio. The switch ratio determines when the controller should behave more like admittance control for accurate motion tracking and when it should move toward impedance control for safer rigid contact. Because demonstration data do not provide ground-truth environment stiffness, we construct switch-ratio labels from measured contact forces and use them to supervise controller-mode prediction. Across box-flipping and line-pressing tasks, URF achieves higher task success rates while reducing failure modes observed with admittance-only execution, including rapid force buildup, large force oscillations, tool breakage, and robot safety stops. These results suggest that contact-aware policies benefit from predicting not only compliant actions but also the controller behavior used to execute them. Project page: https://jiyou384.github.io/urf_project_page/