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Payload generalization on feedforward control actions for trajectory tracking in robots with rigid and elastic joints

Giorgia Pazzi, Giorgio Simonini, Michele Pierallini, Paolo Salaris, Giorgio Grioli, Manolo Garabini, Franco Angelini

arXiv:2610.29356v1cs.ROcs.SYeess.SY

TL;DR

Learning-based feedforward control can struggle to generalize when payloads change, while exact robot dynamics may be difficult to obtain. The paper derives the example-object requirement and presents a controller-independent way to generate feedforward actions for known new payloads; simulations and experiments report tracking performance comparable to ILC across rigid and elastic systems.

  • Problem

    Learning-based control actions often must be relearned when payloads change, and exact robot dynamics can be difficult to obtain, especially with elastic elements.

    Source: §1 · pp. 1–2

  • Method

    The method computes a regressor from feedforward torques for example objects to generate actions for a new payload using its known parameters, without the robot’s dynamic model.

    Source: §1 · p. 2

  • Results

    Across all 28 splits, generalization remained comparable to ILC; Table 5 reports approximately 10% higher average tracking error and lower variability across combinations.

    Source: §4.2 · p. 12

  • Takeaways & Limitations

    Simulations and experiments across rigid and elastic systems support zero-shot payload generalization without repeating learning for each new payload.

    Source: §5 · p. 16

    Ill-conditioned example payload parameters can compromise the numerical stability and accuracy of the regressor matrix estimation.

    Source: §3 · p. 5

Abstract

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Industries employ robots for repetitive tasks due to their high precision and performance, typically achieved through feedforward control actions based on an accurate robot description. However, an exact dynamic model can be difficult to obtain, especially for robots with elastic elements or when the payload changes. Learning-based feedforward approaches are promising for trajectory tracking under model uncertainties, but typically face generalization issues when task parameters vary. This paper proposes a novel method to generalize the feedforward control action with respect to payload parameters, independently of the underlying controller. Firstly, the minimal number of example objects needed for payload generalization is derived. Then, an algorithm is proposed to execute the same trajectory with a new payload, given only its parameters, without knowledge of the robot's dynamic model and even in the presence of elastic joints. The effectiveness of the proposed algorithm is validated in simulations and experiments on tracking tasks with different robots and controllers. Two sets of experiments are performed: on a standard Franka Emika Panda robot, and on a Franka Emika Panda robot equipped with an elastic wrist.

1. Introduction

Learning-based feedforward control can avoid exact robot modeling, but generalizing learned actions when payloads change remains unresolved, particularly for robots with elastic joints. The paper addresses this with controller-independent payload generalization and validates it on rigid and elastic configurations.

1. Introduction

  • Adaptive techniques use model structure to estimate unknown parameters, but high feedback gains can undermine soft-robot compliance and parameter changes can cause suboptimal transients.Even low-gain adaptive schemes remain feedback- and model-based.Source: §1 · pp. 1–2
  • Exact-dynamics feedforward can be difficult in real-world scenarios, motivating model-free, learning-based control strategies.ILC uses data from previous iterations to reduce tracking error without a system model.Source: §1 · p. 2
  • Prior generalization methods address parameters such as stiffness, velocity, endpoints, and trajectories, but not payload dynamic parameters in feedforward control for robots that may have elastic joints.Changing objects can require repeating the learning phase, a time-consuming process that limits scalability.Source: §1 · p. 2
  • The method uses feedforward actions from example objects to generate actions for a new payload from its known parameters, without a robot model or controller-specific assumptions.The paper also derives the minimal number of example objects needed for generalization.Source: §1 · p. 2
  • Validation spans rigid and soft articulated robots, including a Franka Emika Panda with a variable-stiffness actuator wrist and SoftClaw1.The approach relies on payload dynamic parameters rather than the manipulator’s structure or controller.Source: §1 · p. 2

2. Problem statement

The problem is to generalize trajectory-tracking feedforward torques across payloads when the robot model is unknown. The formulation specifies how payload parameters affect the modeled system and sets goals for selecting examples and computing a tracking action.

2. Problem statement

  • The problem statement considers trajectory tracking for robots with rigid and elastic joints.Source: §2 · p. 2

2.1. System model

  • The system model assumes negligible link–motor inertia coupling and non-eccentric motor inertia; payload changes affect link dynamics but leave motor dynamics unchanged.Motor inertia, friction, and stiffness matrices describe the actuators, while the payload modifies the link inertia, Coriolis, and gravity terms.Source: §2.1 · pp. 2–3

2.2. Goal

  • The goals are to identify a minimal set of example payload torques and use them to compute feedforward actions for a feasible desired trajectory with small tracking error.The robot’s nominal model is assumed unknown, while payload parameters and example torques for p payloads are known.Source: §2.2 · p. 3

3. Proposed approach

The approach uses feedforward torques from known example payloads to estimate a regressor and compute tracking torques for a new payload. It requires at least one more example payload than the number of dynamic parameters describing the payload.

  • Payload changes affect the link dynamic parameters, while the motor dynamics remain unaffected.The method decomposes the parameter vector into link, payload, and motor components; the regressor remains unchanged with payload variation.Source: §3 · pp. 3–4
  • Example-payload torques and known payload parameters are used to estimate a regressor, which yields feedforward torques for a new payload.The regressor depends on motion variables, not dynamic parameters, and remains unchanged as payload parameters vary.Source: §3 · pp. 4–5
  • The minimum number of example payloads is r + 1, where r is the number of dynamic parameters describing the payload.Heterogeneous example payloads make the parameter matrix full rank, satisfying the condition needed for generalization.Source: §3 · p. 4
  • The method does not depend on manipulator structure, including its number of degrees of freedom, and avoids identifying the robot’s dynamic parameters.Source: §3 · p. 4
  • Payload-parameter uncertainty affects regressor estimation quadratically in the norm of the inverse parameter matrix, while torque-measurement perturbations propagate linearly.Well-conditioned example-payload parameters help limit this sensitivity.Source: §3 · p. 5

4. Validation

Validation examines payload-generalized feedforward tracking across simulations and real robot systems with rigid and elastic joints, including a fully elastic soft manipulator and Panda robots, using computed-torque and model-free ILC examples.

4. Validation

  • The validation uses model-based computed torque for the elastic manipulator and model-free ILC for the Panda, while generalization uses example torques as data without requiring the robot model.The soft-manipulator simulations cover exact full 10-parameter and reduced 5-parameter payload descriptions; the rigid Panda simulation tests 28 example-test splits using six examples and two held-out objects per split.Source: §4 · p. 6, §4.1 · pp. 7–8, §4.2 · p. 9

4.1. Simulation results: Soft articulated robot

  • 0.00707 versus 0.00807 global RMSE for generalized test-object torques and computed-torque examples in the full 10-parameter study; the corresponding reduced-vector means were 0.00313 versus 0.00112.In both studies, generalized torques matched computed-torque performance on test objects, including eccentric and arbitrarily oriented payloads in the full-vector case and aligned payloads in the reduced-vector case.Source: Figure 3 · p. 7, Figure 4 · p. 8, §4.1 · p. 8

4.2. Simulation results: Rigid system

  • Across all 28 Panda example-test splits, generalized tracking matched ILC on held-out objects and stayed within the example-object error band.The generalized RMSE was slightly higher in some cases because ILC examples retain residual tracking error, which is inherited by the generalized torques.Source: Figure 6 · p. 10, §4.2 · p. 11
  • For Panda payloads, generalization was weaker relative to the example-set error as mass increased, yet matched or improved on ILC for the heaviest objects.Near-zero payloads reduce the effectiveness of the payload-dependent regressor term; the lightest Object 5 reached a maximum relative error of +34% in the reported averages, while the heaviest objects 1 and 4 had negative average relative error.Source: §4.2 · pp. 11–12, Figure 8 · p. 12
  • In rigid-system simulation, generalization increased average tracking error by approximately 10% relative to ILC, with lower variability across payload combinations.Without learning or optimization for test payloads, the method reproduced ILC performance in zero-shot fashion.Source: §4.2 · p. 12

4.3. Experimental results: Rigid system

  • Mean RMSE increased from 0.0128 on ILC example objects to 0.0285 on generalized test objects, while remaining bounded and preserving tracking throughout the task.The gap reflects actuator torque-measurement noise and residual error in approximately known payload parameters, which propagate through the generalization procedure.Source: §4.3 · p. 13, Figure 12 · p. 14, Figure 11 · p. 14

4.4. Experimental results: Panda robot and soft wrist

  • The elastic-wrist experiment used a Panda robot with seven rigid joints and one elastic wrist joint, and learned ILC actions over 100 iterations.The variable-stiffness actuator was operated at fixed stiffness, K = 2.3 N m rad^-1, as a series elastic actuator.Source: §4.4 · p. 14
  • Mean RMSE rose from 0.0362 on example objects to 0.0602 on test objects with the elastic wrist, yet tracking remained bounded across all joints and test objects.The more complex elastic-system dynamics also raised ILC's example-object error relative to the rigid case, and the generalized actions inherited that reference error.Source: §4.4 · pp. 14–15, Figure 16 · p. 15, Figure 15 · p. 15

5. Conclusion

The method generalizes feedforward control inputs to new payloads using their dynamic parameters, without requiring a robot model or repeating learning. Simulations and Panda-based experiments validate it across rigid and elastic-joint systems, while trajectory changes remain outside its current scope.

5. Conclusion

  • The model-independent method generalizes feedforward control inputs to new payloads using their dynamic parameters, without repeating the learning process.It is designed for systems with rigid and elastic joints.Source: §5 · p. 16
  • Validation covered a 3-DoF soft-articulated manipulator, a rigid Panda, and a Panda with an elastic wrist, using simulations and physical experiments.The 3-DoF simulation used computed-torque control; the other setups derived example torques using ILC.Source: §5 · p. 16
  • The procedure must be repeated for trajectory changes; future work could address different endpoints and payloads with inaccurately known parameters.Source: §5 · p. 16

CRediT authorship contribution statement

The contribution statement assigns writing, methodology, validation, software, analysis, and conceptualization roles across the authors.

CRediT authorship contribution statement

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