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\%.

翻译：物理人机交互（pHRI）要求在未规划的接触中同时实现轨迹精度与顺应性安全。经典阻抗控制在持续人体力作用下会产生非零稳态位置误差（即作用力除以任务刚度），而积分作用仅在狭窄的稳定增益范围内才能降低该误差。本文提出一种双层阻抗模型预测控制（Impedance MPC）以解决这一矛盾。第一层通过解析方法消除重力、科氏力及任务空间惯性，将残差对象简化为具有恒定状态转移矩阵的构型无关双积分器。第二层以100 Hz频率求解包含30个变量的凸二次规划问题，利用该恒定结构实现自由响应矩阵的预计算；通过增广卡尔曼滤波器估计持续扰动状态，从而提供形式化的零稳态误差保证。采用零空间逆势函数与任务空间工作空间投影，确保在整个测试工作空间内满足关节极限安全约束。在7自由度Franka FR3机器人上的实验表明：在持续15 N力作用下，采用卡尔曼增广的阻抗模型预测控制可实现低于0.05 mm的稳态误差（相比经典阻抗控制的44.8 mm降低超过800倍），在三维空间四个圆形轨迹上的跟踪精度达亚毫米级，并对测量噪声及高达30%的惯性失配表现出优异的鲁棒性。