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Learning-Enhanced Observer for Sensorless Task-Null-Space Compliant Control
Nuo Chen, Ya-Jun Pan, Onur Toker
TL;DR
pHRI requires robust task motion alongside compliance with human disturbance, while existing approaches often treat these objectives separately and rely on force sensors. The paper combines an NN-enhanced observer, task-null-space decomposition, and hybrid pose-and-force control; experiments report improved force estimation and simultaneous tracking with compliant behavior. The current approach depends on offline training data and has a limited experimental range of trajectories and disturbance conditions.
Problem
pHRI needs accurate task execution and compliant response to human interaction, while many approaches separate robustness from compliance or rely on force/torque sensors.
Source: §I · p. 1Method
The framework combines an NN-enhanced momentum observer using task-null-space decomposition with hybrid pose-and-force control and null-space compliance.
Source: §I · p. 2Results
During human disturbances, the proposed observer reduced RMSE by 60.1% and 53.5%, respectively, versus the learning-based observer using full joint velocity.
Source: A. Estimation Results · p. 8Takeaways & Limitations
The experiments report simultaneous task-space pose tracking, force regulation, and compliant null-space behavior without requiring force/torque sensor measurements.
Source: §I · p. 2, §VI · p. 9The learned observer depends on offline training data, and experiments cover a relatively limited range of trajectories and disturbance conditions.
Source: §VI · p. 9
Abstract
from arXiv · showhide
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.
I. INTRODUCTION
pHRI requires accurate task execution alongside compliance with human disturbances, yet existing approaches often separate robustness and compliance or rely on force sensors. This work combines a learning-enhanced observer and hybrid controller, with task-null-space decomposition to support both objectives.
I. INTRODUCTION
- pHRI requires accurate position, orientation, and force tracking while remaining compliant when unexpected human interaction occurs.The paper frames these as simultaneous task-execution, interaction-estimation, and disturbance-response objectives.Source: §I · p. 1
- Existing approaches often switch between robustness and compliance controllers, and many pose-and-force studies are limited to 2D-flat surfaces.The paper motivates simultaneous task tracking and compliant motion under human-applied disturbance.Source: §I · pp. 1–2
- The framework combines momentum-observer estimation, neural-network compensation, and task-null-space decomposition with a hybrid controller for task tracking and compliant interaction.Task-space velocity informs the NN-based force estimation, while null-space velocity supports compliant control.Source: §I · p. 2, Figure 1 · p. 2
A. Robot Manipulator Dynamics
- The joint-space model represents commanded torque and lumped disturbance torque, with the latter comprising friction, unmodeled dynamics, and external torque.The manipulator used in the study is a 7-DOF Franka Emika robot with a 3 Kg payload and a 1 kHz torque-control interface.Source: A. Robot Manipulator Dynamics · pp. 2–3
- The Cartesian model expresses end-effector dynamics using Cartesian parametric matrices and task-space input and disturbance.The end-effector state includes position and quaternion orientation, with velocity and acceleration represented in six dimensions.Source: A. Robot Manipulator Dynamics · p. 3
B. End-Effector Configuration
The experimental setup uses a 7-DOF Franka Emika manipulator with a custom end-effector and a force sensor for observer data collection and validation.
B. End-Effector Configuration
- The end-effector is configured for a wiping task using a sponge and a force sensor.The sensor is mounted with connectors, and the end-effector has a fixed offset along the interaction normal.Source: B. End-Effector Configuration · p. 3
- A 7-DOF Franka Emika manipulator is used with a custom end-effector for the experiments.The setup replaces the gripper with two connectors, a 3D force sensor, and a sponge for wiping.Source: Figure 2 · p. 3, B. End-Effector Configuration · p. 3
- The end-effector sensor collects data for observer evaluation and validates the estimated force.The setup uses an OptoForce three-axis optical force sensor; the end-effector has a fixed 0.09 m offset along the normal direction.Source: B. End-Effector Configuration · p. 3, Figure 2 · p. 3
III. OBSERVER DESIGN
The observer uses generalized momentum to estimate external wrench without joint-acceleration estimates or inversion of the robot inertia matrix. Its conventional form is affected by sim-to-real differences, motivating neural-network compensation.
A. Momentum Observer
- The generalized momentum observer avoids noisy joint-acceleration estimates and inversion of the robot inertia matrix when estimating force.The observer is designed to replace the force sensor during tracking.Source: A. Momentum Observer · p. 3
- The conventional momentum observer cannot reliably replace a force sensor in practice because joint friction and unmodeled dynamics affect its estimation.The study contrasts the same circular trajectory without external wrench in simulation and the real world.Source: A. Momentum Observer · p. 3, Figure 3 · p. 4
- In real-world tests, the conventional observer output is affected by manipulator posture, unlike its performance under ideal simulation conditions.The paper introduces an NN to compensate for this simulation-to-reality gap.Source: A. Momentum Observer · p. 4, Figure 3 · p. 4
B. Proposed Observer
The observer augments a momentum-based force estimate with a neural-network correction, using task-space joint velocity to reduce the effect of disturbance-induced motion. It requires no joint-torque or task-space force sensors during real-time estimation.
B. Proposed Observer
- The observer adds an NN correction Φ(q, ˙q) to the momentum-observer force estimate to compensate for force-estimation error.The NN input is q and task-space joint velocity; its three-dimensional output represents the difference between sensor force and momentum-observer force.Source: B. Proposed Observer · p. 4
- The NN receives task-space joint velocity rather than full joint velocity, reducing the influence of disturbance-induced motion on learned force compensation.The null-space component represents internal redundant motion and does not contribute to end-effector velocity.Source: B. Proposed Observer · p. 4
- The observer needs neither joint-torque sensors nor task-space force sensors during real-time force estimation.The end-effector force sensor is used only for offline data collection and validation.Source: B. Proposed Observer · p. 4
IV. CONTROLLER DESIGN
The controller combines one-dimensional admittance along the end-effector normal with Cartesian pose and force control. It modifies the reference along the interaction direction while tracking position, orientation, and contact force.
A. Admittance Control
- A one-dimensional admittance controller along the end-effector normal generates compliant displacement from estimated z-axis force and desired contact force.The displacement follows a second-order mass-spring-damper model.Source: A. Admittance Control · p. 4
- The admittance controller modifies the reference position only along the interaction direction, leaving the nominal trajectory unchanged in orthogonal directions.It accounts for both the admittance displacement and the fixed 0.09 m sensor offset; the displacement is limited to 0.02 m.Source: A. Admittance Control · p. 5
B. Task-Space Pose and Force Controller
- The Cartesian pose controller uses position and quaternion-based orientation errors to track the desired pose.Its feedback design is inspired by a non-singular terminal sliding mode controller.Source: B. Task-Space Pose and Force Controller · p. 5
- A proportional-derivative controller generates the commanded interaction force, which is applied along the interaction direction.The pose and force joint-torque commands are combined.Source: B. Task-Space Pose and Force Controller · p. 5
- The task-space controller simultaneously regulates Cartesian position and orientation while controlling interaction force along the contact direction.It combines a six-dimensional pose-tracking input with a force input along the interaction direction, then maps them to joint space.Source: B. Task-Space Pose and Force Controller · p. 5
C. Null-Space Compliant Control
The controller uses redundant joint motion for compliance without changing the end-effector task. A spring-damper torque is projected into the null space and combined with task-space commands.
C. Null-Space Compliant Control
- A null-space compliant controller uses redundant motion to improve robot compliance without affecting the end-effector task.The task-space objective does not uniquely determine joint motion, leaving redundancy available for posture control.Source: C. Null-Space Compliant Control · p. 6
- A virtual spring-damper controller generates raw null-space torque from the desired null-space joint posture.The damping coefficient is selected as Dn = 2√Kn.Source: C. Null-Space Compliant Control · p. 6
- The commanded torque combines task-space pose and force terms, projected null-space torque, and Coriolis and gravity feedforward.The raw null-space torque is projected into the null space before being applied.Source: C. Null-Space Compliant Control · p. 6
D. Stability Analysis
The stability analysis models imperfect disturbance compensation as a bounded residual disturbance. Under the stated gain condition, the Lyapunov function is non-increasing and the closed-loop sliding dynamics remain stable.
D. Stability Analysis
- The stability argument forms the closed-loop task-space dynamics after nominal Coriolis and gravity terms are compensated by feedforward.It then substitutes the pose controller and uses a Lyapunov candidate positive definite with respect to the sliding variable.Source: D. Stability Analysis · p. 6
- The residual compensation disturbance captures the mismatch left by force-estimation errors, modeling uncertainties, and other unmodeled effects.It is defined as d = M̄^-1∆u and assumed uniformly bounded by a known constant.Source: D. Stability Analysis · p. 6
- With gains satisfying the stated condition, the Lyapunov function is non-increasing under bounded disturbance and the closed-loop sliding dynamics remain stable.The stabilizing control term dominates force-estimation errors, interaction disturbances, and unmodeled dynamics.Source: D. Stability Analysis · p. 6
V. PERFORMANCE EVALUATION
The performance evaluation used a 7-DOF Franka Emika manipulator. The framework ran in real time without force-sensor feedback.
V. PERFORMANCE EVALUATION
- Experiments used a 7-DOF Franka Emika robotic manipulator with a custom-designed end-effector.The experiments were conducted on a desktop equipped with an Intel i7 CPU and Intel UHD Graphics 630 GPU.Source: §V · p. 6
- Figure 4 compares three observer estimates with sensor force during human-applied disturbances, highlighting periods around 14 s and 27 s.The compared approaches are the conventional momentum observer, a learning-based observer using full joint velocity, and the proposed observer.Source: Figure 4 · p. 7
- The framework ran in real time without force-sensor feedback for control.The observer network was integrated into the control loop, with total computation time below 1 ms.Source: §V · p. 7
A. Estimation Results
The proposed observer improved force-estimation accuracy over the full-velocity learning observer, with larger RMSE reductions during human-disturbance periods. Learning-based observers also reduced errors relative to the conventional momentum observer.
A. Estimation Results
- The comparison used force measurements during a bowl-wiping task with manual disturbances applied to the robot body.Only z-direction force was presented because interaction force was primarily applied along the end-effector z-axis.Source: A. Estimation Results · p. 7
- The proposed observer achieved 0.729 N overall RMSE and 1.892 N maximum error, reducing these by 24.1% and 38.0% versus the full-velocity learning observer.Both learning-based approaches substantially reduced estimation error compared with the conventional momentum observer.Source: Table I · p. 7, A. Estimation Results · p. 8
- The task-space-input network reduced validation MSE by 2.15%, RMSE by 1.08%, and MAE by 7.21% relative to the full-velocity network.Its RMSE also decreased by 10.78%, 12.43%, and 16.92% under the 1, 2, and 3 N conditions, respectively.Source: A. Estimation Results · p. 7
- The conventional momentum observer showed large deviations from measured force under posture changes and body disturbances, while both learning-based observers estimated force closer to the sensor measurement.The conventional observer cannot distinguish joint friction and model errors from end-effector interaction force.Source: A. Estimation Results · p. 7
- During two human-disturbance periods, RMSE fell from 2.016 N to 0.804 N and from 0.878 N to 0.408 N, improvements of 60.1% and 53.5%.The paper attributes the reduced disturbance influence to replacing full joint velocity with its task-space component.Source: A. Estimation Results · p. 8
B. Tracking Performance
Across two reference trajectories, the controller maintained bounded position, orientation, and force tracking errors. The tests covered different path shapes and motion directions while regulating pose and z-direction interaction force simultaneously.
B. Tracking Performance
- During both trajectories, the controller simultaneously regulated end-effector pose and interaction force along the z direction.Figure 5 presents translational, orientation, and z-direction force tracking errors for R1 and R2.Source: B. Tracking Performance · p. 8
- For R1, force tracking RMSE was 0.464 N; position RMSEs were 0.732, 0.888, and 1.403 cm, and orientation RMSEs were 0.018, 0.026, and 0.012 rad.R1 was a circular path in the x-y plane at constant z, with orientation varying during motion.Source: B. Tracking Performance · p. 8, Figure 6 · p. 8
- For R2, force tracking RMSE was 0.876 N; position RMSEs were 0.179, 0.990, and 0.506 cm, and orientation RMSEs were 0.047, 0.006, and 0.008 rad.R2 was a rounded trapezoidal path in the y-z plane at constant x, with orientation adjusted along the path.Source: B. Tracking Performance · p. 8, Figure 6 · p. 8
- For both tasks, position tracking RMSE stayed below 1.5 cm, orientation tracking RMSE below 0.05 rad, and force tracking RMSE below 0.9 N.The two tasks had different error distributions, but tracking errors remained consistently bounded.Source: B. Tracking Performance · pp. 8–9, Table II · p. 9
VI. CONCLUSION
The framework combines a learned wrench observer and task-null-space decomposition with a controller for robust task-space tracking and compliant interaction. Experiments report reduced observer error under human disturbance and simultaneous pose tracking, force regulation, and compliant null-space behavior, while experiments remain limited in scope and the observer depends on offline training data.
VI. CONCLUSION
- 0.729 N overall RMSE; under human disturbance, the observer reduces RMSE by 60.1% and 53.5% compared with the learning-based observer.The observer combines an NN with task-space/null-space joint-velocity decomposition and is less affected by disturbances applied to the robot body.Source: §VI · p. 9
- Using the estimated interaction force, the controller achieves simultaneous task-space pose tracking, force regulation, and compliant null-space behavior.Source: §VI · p. 9
- The learned observer depends on offline training data, and experiments cover a relatively limited range of trajectories and disturbance conditions.Future work proposes adaptive and online learning and evaluation in more complex, unstructured pHRI tasks.Source: §VI · p. 9