Mass-Adaptive Admittance Control

• The paper introduces mass-adaptive admittance control, a technique that dynamically estimates and compensates for unknown payload mass to maintain compliant robotic manipulation.
• It employs real-time payload estimation using sensor filtering and adaptive excitation forces, significantly reducing end-effector sag and tracking errors.
• Experimental validation shows marked improvements in stability and accuracy, with RMSE reductions from over 40 mm to approximately 2 mm under low stiffness conditions.

Mass-adaptive admittance control is a class of robot control architectures in which the virtual dynamical parameters—particularly inertia—within the admittance loop adapt to compensate for unknown or time-varying payload mass. This paradigm enables compliant manipulators to maintain stable, accurate tracking and task execution in environments characterized by uncertainty in payload properties, especially mass and, in recent developments, center-of-mass (CoM) offset. Mass-adaptive admittance controllers integrate real-time estimation of payload properties with adaptive excitation forces in the admittance law, thereby decoupling the controller’s response to exogenous disturbances from quasi-static effects induced by unknown payloads. Rigorous experimental evaluation demonstrates strong gains in compliance, stability, and end-effector accuracy relative to standard admittance control, particularly where low virtual stiffness is desired.

1. Control Objectives and Admittance Modeling

The central objective of mass-adaptive admittance control is to achieve reliable, compliant robotic manipulation in the presence of payloads with unknown or variable mass. Conventional admittance controllers with fixed virtual mass, damping, and stiffness suffer significant degradation in accuracy—most notably end-effector sag—if subjected to unmodeled payload-induced forces (Gholampour et al., 22 Apr 2025, Gholampour et al., 21 Apr 2026). To address this, mass-adaptive schemes pursue:

• On-line estimation and compensation for unknown payload mass.
• Preservation of closed-loop stability and compliance.
• Suppression of static and dynamic offset errors induced by gravity or inertial forces.

The canonical admittance law for a Cartesian space manipulator is

$$M_a\,(\ddot{\bm p}_a - \ddot{\bm p}_0) + B_a\,(\dot{\bm p}_a - \dot{\bm p}_0) + K_a(\bm p_a - \bm p_0) = \bm F_{ext}(t)$$

where $\bm p_a$ is the virtual (commanded) end-effector pose, $M_a$, $B_a$, $K_a$ are the virtual mass, damping, and stiffness, and $\bm F_{ext}(t)$ is the measured external wrench.

When a payload of unknown mass induces an unmodeled gravitational force $m_u g$, a static sag proportional to $m_u/K_{zz}$ is observed. Mass-adaptive admittance control corrects for this effect by modifying the admittance law to include an adaptive excitation term that cancels the gravity- and inertia-induced wrench, yielding

$$M_a\,(\ddot{\bm p}_a - \ddot{\bm p}_0) + B_a\,(\dot{\bm p}_a - \dot{\bm p}_0) + K_a(\bm p_a - \bm p_0) - \bm F_{exc}(t) = \bm F_{ext}(t).$$

(Gholampour et al., 22 Apr 2025, Gholampour et al., 21 Apr 2026)

2. Real-Time Payload Mass Estimation

A critical enabler of mass-adaptive admittance control is the on-line estimation of the unknown payload mass using filtered force-torque and accelerometer data. During non-contact, free-space transport, the vertical component of Newton’s second law yields

$$(m_g + m_u)\,\ddot{p}_z + (m_g + m_u)g + f_{sens,z} = 0$$

where $\bm p_a$0 is gripper mass, $\bm p_a$1 is unknown payload mass, $\bm p_a$2 is the vertical force from the wrist sensor, and $\bm p_a$3 is gravity. Algebraic manipulation provides an instantaneous estimator: $\bm p_a$4 This estimator is implemented sample-wise in the admittance loop, with both force and acceleration low-pass filtered to suppress noise. The total (gripper plus payload) estimated mass is then $\bm p_a$5.

This estimated mass parameterizes the excitation force for dynamic compensation: $\bm p_a$6 (Gholampour et al., 22 Apr 2025, Gholampour et al., 21 Apr 2026)

Alternative approaches include iterative learning methods in which mass, damping, and stiffness parameters are updated via ILC laws based on force-tracking error over repeated trials (Zhou et al., 2024), and adaptive filtering approaches such as Unscented Kalman Filters that treat the virtual mass and damping as online-tunable parameters based on performance cost functions (Schperberg et al., 2022).

3. Integration of Mass Adaptation into the Admittance Controller

The estimated mass and corresponding excitation force are tightly integrated with the admittance law. Substituting the adaptive force compensation term yields a “mass-adaptive” admittance transfer function in which the robot’s compliant response is decoupled from persistent, payload-induced wrenches. This adaptation is dynamic: whenever the estimated payload mass changes, the excitation term is recomputed in real time.

The velocity command sent to the robot is computed by integration of the compensated acceleration, and the reference pose is updated when the desired waypoint is reached. Typical implementations operate at control rates of 250–1000 Hz with windowed data filtering.

For currently demonstrated schemes, compensation is implemented primarily along the gravitational axis (usually $\bm p_a$7); extension to full 6-DOF mass/inertia estimation (mass and CoM offsets) has recently been developed (Gholampour et al., 21 Apr 2026).

4. Stability Considerations

Closed-loop stability in mass-adaptive admittance control follows from two sources. For algebraic, sample-wise mass estimation (e.g., (Gholampour et al., 22 Apr 2025)), stability is analyzed by inspecting the roots of the closed-loop characteristic equation: $\bm p_a$8 where $\bm p_a$9 is the inner-loop robot velocity controller, and $M_a$0, $M_a$1 are the true and estimated payload masses. Provided admittance gains and the inner-loop controller are appropriately selected (critical damping, mass estimated within reasonable error), bounded-input/bounded-output stability is retained.

In methods with adaptive gain update rules (e.g., UKF (Schperberg et al., 2022), ILC (Zhou et al., 2024)), stability is assured by positive-definiteness constraints on the gain matrices, projection onto physically plausible parameter sets, and/or objective functions penalizing violations of force/torque or kinematic safety limits. For adaptation with provable passivity (e.g., (Landi et al., 2017)), energy-tank or passivity-based inequalities are employed to constrain inertia updates, ensuring the controller never injects more energy than is physically dissipable by damping.

5. Experimental Validation and Performance

Empirical evaluation establishes the quantitative benefits of mass-adaptive admittance controllers. In (Gholampour et al., 22 Apr 2025), a UR5e manipulator equipped with a wrist force/torque sensor and accelerometer performed a six-waypoint pick-and-place task with payloads of ≈1.5 kg. Representative results:

Exp.	Stiffness $M_a$2 (N/m)	Mass Comp.	Task Success	Sag $M_a$3 (mm)	RMSE$M_a$4 (mm)
1	1800	No	Fail	8.1	9.53
2	2500	No	Success	3.5	4.71
3	300	Yes	Success	<3.5	1.99
4	300	No	Fail	46.8	20.58

With mass compensation, stable and accurate tracking (RMSE$M_a$5 ≈ 2 mm) was achieved even with very low virtual stiffness. In contrast, uncompensated systems exhibited >40 mm sag and large tracking error at low stiffness, or required stiff, less compliant settings to remain stable.

Wrench-aware extensions combining mass and CoM estimation (Gholampour et al., 21 Apr 2026) yield transport and placement RMSE under 3.5 mm for multi-object stacking tasks, reducing placement errors from ∼20 mm (uncorrected) to ∼3 mm when compensating both mass and CoM offset.

Adaptive admittance controllers based on iterative learning (Zhou et al., 2024) achieve ~98% reduction in force-tracking RMSE versus fixed-parameter baselines.

UKF-based adaptation (Schperberg et al., 2022) demonstrated 40–70% improvement in wrench-tracking norms and fast convergence within 1 s for grasping and ≲10 s for complex wrench tracking.

6. Limitations and Implementation Guidelines

While mass-adaptive admittance controllers substantially improve performance with unknown payloads, limitations remain:

• The standard estimator presumes largely vertical manipulation and bias-free acceleration. Sudden accelerations or contacts induce transient estimation errors.
• Currently, most schemes estimate only mass (scalar) or, in recent works, the mass and static CoM offset. Full estimation and compensation of the payload inertia tensor or dynamic effects remains an open field.
• Filtering windows and controller update rates trade latency versus noise suppression.

Key implementation guidelines (as documented in (Gholampour et al., 22 Apr 2025, Zhou et al., 2024, Landi et al., 2017)):

• Set virtual mass near the expected total mass (gripper + typical payload).
• Stiffness should be low enough for compliance but high enough to restrict sag prior to compensation (e.g., 300–500 N/m).
• Damping is selected for critical or slight over-damping ($M_a$6).
• Apply filtering windows (20–50 ms) to sensor and acceleration signals.
• Impose physical bounds and safety constraints during parameter adaptation.

Potential extensions include adaptation of the full 6 × 6 mass-inertia matrix, adaptive filtering/gradient-descent estimation dynamics, and generalization to multi-axis and multi-platform (including aerial) applications.

7. Connections to Related Adaptive and Passivity-Based Control

Mass-adaptive admittance control generalizes earlier adaptive strategies in admittance control — such as passivity-based inertia and damping adaptation (Landi et al., 2017), iterative learning of virtual parameters (Zhou et al., 2024), and stochastic estimation approaches (Schperberg et al., 2022). Essential distinctions in the mass-adaptive class include real-time, sample-wise payload estimation and the explicit introduction of feedforward excitation forces to decouple the virtual system’s behavior from persistent, payload-induced disturbances.

Recent research highlights extensions to wrench-aware schemes that also infer and compensate for the center-of-mass offset, a critical factor when manipulating unknown or asymmetric objects (Gholampour et al., 21 Apr 2026). This suggests a pathway toward fully wrench/geometry-aware compliant control.

Leading research is now exploring integration of these schemes with multi-contact force tracking, collaborative human-robot interaction, and dexterous manipulation under strong dynamic uncertainty. The convergence of adaptive identification, robust force estimation, and compliant control architectures forms a rapidly developing foundation for next-generation robotic autonomy in unstructured environments.