Learning-Enhanced Observer for Sensorless Task-Null-Space Compliant Control

Nuo Chen; Ya-Jun Pan; Onur Toker

cs.ROOct 20, 2026

Learning-Enhanced Observer for Sensorless Task-Null-Space Compliant Control

Authors: Nuo Chen, Ya-Jun Pan, Onur Toker

Organizations: Advanced Control and Mechatronics Lab, Department of Mechanical Engineering, Dalhousie University, Halifax, B3H 4R2, Canada · Department of Computer Engineering, Florida Polytechnic University, Lakeland, FL 33805, United States

Abstract

This paper presents a novel framework integrating a robust wrench observer with a hybrid pose and force controller for physical Human-Robot Interaction (pHRI). In pHRI tasks, robots are expected to perform task-space motions robustly while remaining compliance with human disturbance, which proposes distinct control objectives. Most existing approaches focus mainly on either robustness or compliance and rely on force sensors for real-time tracking. To address these limitations, we propose a novel framework with the following key contributions. Firstly, a neural network (NN) is trained to improve the observer performance by compensating for system friction and unmodeled dynamics. Secondly, a task-null-space decomposition is applied to separate the joint velocity and reduce the effect of the human disturbance on the observer. Finally, a hybrid pose and force controller is introduced to achieve the end-effector pose and force tracking. Experimental results demonstrate that the proposed framework provides robust and accurate wrench estimation while maintaining reliable pose and force tracking performance. The proposed approach offers an effective solution and framework for pHRI without the need of force/torque sensor measurements which can be applied to many robotic manipulator platforms which do not have force/torque sensors.

Figures & tables

Fig. 1: Overview of the proposed framework. The observer estimates the end-effector force using a momentum observer and NN compensation. A task-null-space decomposition separates the joint velocity $\dot{\bm{q}}$ into the task-space velocity $\dot{\bm{q}}_{t}$ and null-space velocity $\dot{\bm{q}}_{n}$ . The task-space velocity $\dot{\bm{q}}_{t}$ is sent to the NN to reduce the effect of human disturbance on force estimation, while $\dot{\bm{q}}_{n}$ is used for null-space compliant control. The proposed hybrid pose and force controller provides reliable position, orientation, and force tracking while maintaining compliance in the null-space.

Panel of Figure 2 — Fig. 2: Hardware Setup: (a) A 7-DOF Franka Emika robotic manipulator in the Advanced Control and Mechatronics Laboratory, Dalhousie University. (b) An end-effector installed with force sensor for data collection and validation.

Panel of Figure 3 — Fig. 3: Conventional momentum observer sim-to-real gap. (a) Test in Gazebo. (b) Test in real world. (c) Observer output difference between the simulation and real world.

Fig. 4: Comparison of the end-effector force estimation performance under human applied disturbances. The conventional momentum observer, the learning-based observer using the full joint velocity, and the proposed observer were compared with sensor force. The enlarged regions within box lines highlight the estimation performance during human disturbance periods at around $T=14\ s$ and $27\ s$ respectively.

Observer	Overall	Region 1	Region 2	Maximum
Observer	RMSE(N)	RMSE(N)	RMSE(N)	Error(N)
$\hat{F}_{m}^{z}$	7.513	9.334	3.103	12.253
$\hat{F}_{\Phi(\bm{q},\dot{\bm{q}})}^{z}$	0.960	2.016	0.878	3.054
$\bm{\hat{F}_{\Phi(\bm{q},\dot{\bm{q}}_{t})}^{z}}$	0.729	0.804	0.408	1.892

TABLE I: Comparisons of the end-effector force estimation performance

Panel of Figure 6 — Fig. 5: Controller tracking performance with two reference trajectories (a) $R_{1}$ and (b) $R_{2}$ . The translational position tracking errors $P^{x}$ , $P^{y}$ , and $P^{z}$ are along the x, y and z directions. The orientation tracking errors $O^{\psi}$ , $O^{\theta}$ , and $O^{\phi}$ are yaw, pitch, and roll. The force tracking errors $F^{z}$ are along the z direction.

Panel of Figure 7 — Fig. 6: Reference trajectories $R_{1}$ and $R_{2}$ . (a) $R_{1}$ is a circular trajectory and (b) $R_{2}$ is a rounded trapezoidal trajectory.

Tracking Error	$R_{1}$ RMSE	$R_{2}$ RMSE
$F^{z}$ (N)	0.464	0.876
$P^{x}$ (cm)	0.732	0.179
$P^{y}$ (cm)	0.888	0.990
$P^{z}$ (cm)	1.403	0.506
$O^{\psi}$ (rad)	0.018	0.047
$O^{\theta}$ (rad)	0.026	0.006

TABLE II: Tracking Performance

Robotics

Robotics studies the design and control of machines that perceive, move, and act in physical environments.

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Toward Interaction Dynamics: A Predictive Framework for Safe Physical Human Robot Interaction

Yongyan Cao, Jinshan Tang

Voryx Robotics LLC, San Jose, CA 95136, USA · Department of Health Administration and Policy, George Mason University, Fairfax, VA, USA

Model Predictive Control Human-Robot Interaction

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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.

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