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

cs.ROOct 21, 2026

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

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

Organizations: Centro di Ricerca “Enrico Piaggio”, Università di Pisa, Largo Lucio Lazzarino 1, Pisa, 56126, Italy · Dipartimento di Ingegneria dell’Informazione, Università di Pisa, Via G. Caruso 16, Pisa, 56122, Italy · Soft Robotics for Human Cooperation and Rehabilitation, Fondazione Istituto Italiano di Tecnologia, Genoa, 16163, Italy

Abstract

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.

Figures & tables

Fig. 1 : Scheme of the proposed payload generalization method. The figure shows the main steps of the procedure: first, feedforward torques are collected for a set of example objects with known parameters; then, these data are used to compute the regressor matrix that enables the generation of feedforward control actions for any new payload with known parameters.

Fig. 2 : Schematic representation of the simulated 3-DoF soft articulated manipulator, actuated with SEAs.

Object [i]	shape	mass [ $\mathrm{k}\mathrm{g}$ ]	$\\|l_{c_{i}}\\|$ [ $\mathrm{m}$ ]	tilt [ $\mathrm{\SIUnitSymbolDegree}$ ]
0	–	0	0.00	0.0
1	box	3	0.17	40.8
2	cylinder	6	0.25	43.7
3	tube	9	0.32	72.6
4	ellipsoid	12	0.21	95.2
5	cone	15	0.38	92.7

Table 1: Object parameter values for the full 10-parameter payload description of the 3-DoF soft articulated manipulator. For each object,

\|l_{c_{i}}\|

is the distance of the center of mass from the origin of the end-effector frame, and the tilt is the rotation of the object principal axes w.r.t. the same frame.

Fig. 3 : Simulation 3-DoF soft articulated manipulator with the full 10-parameter payload description: comparison of desired and generalized torques performance.

Object [i]	mass [ $\mathrm{k}\mathrm{g}$ ]	length [ $\mathrm{m}$ ]	width [ $\mathrm{m}$ ]	height [ $\mathrm{m}$ ]
0	0	0.0	0.0	0.0
1	30	0.32	0.16	0.11
2	10.82	0.15	0.15	0.05
3	4.16	0.92	0.46	0.31
4	22.67	0.47	0.16	0.24
5	1.59	0.63	0.32	0.21

Table 2: Object parameter values for the reduced 5-parameter payload description of the 3-DoF soft articulated manipulator.

Fig. 4 : Simulation 3-DoF soft articulated manipulator with the reduced 5-parameter payload description: comparison of desired and generalized torques performance.

Fig. 5 : Simulation of Panda robot: the subplots show the ILC RMSE convergence over 300 iterations for the case of no payload (Object 0) and for all the remaining objects (Object 1-7).

Object [i]	mass [ $\mathrm{k}\mathrm{g}$ ]	length [ $\mathrm{m}$ ]	width [ $\mathrm{m}$ ]	height [ $\mathrm{m}$ ]
0	0	0	0	0
1	2.7	0.035	0.062	0.027
2	0.6	0.073	0.025	0.054
3	1.8	0.036	0.071	0.043
4	3.0	0.065	0.022	0.057
5	0.3	0.032	0.079	0.014

Table 3: Objects parameters values for simulation tests on the Franka Emika Panda manipulator.

Joint	1	2	3	4	5	6	7
$k_{p}$	10	20	20	10	4	4	4
$k_{v}$	1	2	2	1	0.4	0.4	0.4
$k_{a}$	0.1	0.2	0.2	0.1	0.04	0.04	0.04

Table 4: ILC controller gains.

Fig. 6 : Tracking RMSE in Panda robot simulation over the

28

example-test combinations. In each subplot, labeled

\textnormal{T}i\textnormal{-}j

, objects

i

and

j

are used as test objects while the remaining six form the example set; the light blue bars report the ILC RMSE on the six example objects, the dark blue bars the ILC RMSE on the two test objects, and the red bars the RMSE of the payload generalization on the same two test objects.

	mean RMSE	STD
ILC	0.001916	0.000658
Payload generalization	0.002108	0.000496

Table 5: Summary of mean RMSE and Standard Deviation (STD) across all example-test splits.

Fig. 7 : Simulation of Panda robot: comparison between the desired trajectory and the actual trajectories obtained with ILC and generalized torques on Object 7 for the example-test split T6-7.

Panel of Figure 13 — Fig. 8 : Generalization performance for the simulated Panda robot over the $28$ example-test combinations, with objects ordered by increasing mass. On the left (a), the ratio $\rho$ compares the generalization against the example-object set. On the right (b), the relative error $\delta$ quantifies the error introduced by the generalization relative to ILC on the same test object. The vertical bars span the minimum and maximum values attained over the $N_{o}=7$ splits in which the object belongs to the test set. The dashed line marks parity ( $\rho=1$ , $\delta=0$ ) and the gray line is the linear fit versus mass.

Object [i]	mass [ $\mathrm{k}\mathrm{g}$ ]	$cm_{z}$ [ $\mathrm{m}\mathrm{m}$ ]	$I_{xx}$ [ $\mathrm{g}\text{\,}{\mathrm{m}}^{2}$ ]	$I_{yy}$ [ $\mathrm{g}\text{\,}{\mathrm{m}}^{2}$ ]	$I_{zz}$ [ $\mathrm{g}\text{\,}{\mathrm{m}}^{2}$ ]
0	0	0	0	0	0
1	0.142	36	0.126	0.126	0.126
2	1.399	74	2.65	2.74	0.284
3	0.740	75	1.42	1.42	0.0710
4	0.442	50	0.460	0.559	0.283
5	0.942	50	0.840	0.910	0.180

Table 6: Parameter values of objects used in experiments with the Franka Emika Panda robot and the Panda robot equipped with a soft wrist.

Fig. 9 : Objects set used for real-world experiments.

Fig. 10 : Experiment on real-world Panda robot: the subplots show the ILC RMSE reduction over 150 iterations for all six example objects.

Fig. 11 : Experiment on real-world Panda robot: comparison between desired trajectory and actual trajectories obtained with ILC and generalized torques.

Fig. 12 : Experiment on real-world Panda robot: comparison of ILC-based and generalized torques performance.

Panel of Figure 19 — Fig. 13 : System setup for the final experiments: the Panda robot is equipped with an elastic wrist. On the left, the soft wrist is connected to the gripper for object grasping. On the right, the system performs trajectory tracking while holding an object.

Fig. 14 : Experiment on Panda manipulator with elastic wrist: the subplots show the ILC RMSE reduction over 100 iterations for all six example objects.

Fig. 15 : Experiment on Panda manipulator with elastic wrist: comparison between desired trajectory and actual trajectories obtained with ILC and generalized torques.

Fig. 16 : Experiment on Panda manipulator with elastic wrist: comparison of ILC-based and generalized torque performance.

Fig. 17 : Photo sequence of the Panda robot with an elastic wrist tracking the desired trajectory while carrying Object 8, using the control action computed with the generalized torque method.

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Model-based control can achieve reliable task performance, but its effectiveness depends on the accuracy of the underlying model. Robots operating under model uncertainty must often adapt to previously unseen payloads, objects, and interaction dynamics to complete a task successfully. Conventional approaches typically rely on a dedicated task- and control-agnostic excitation phase for estimating physics parameters, delaying task execution and collecting potentially irrelevant data. In this paper, we instead consider zero-shot task execution under parametric uncertainty, where online model learning and control proceed concurrently during task execution. Our approach formulates reference generation within a dual control framework to produce task-relevant, informative trajectories that reduce parameter uncertainty in directions critical to task success. We predefine a feedback policy with an explicit parameter adaptation law and optimize the reference through the resulting adaptive closed-loop dynamics. We propose two formulations: 1) minimizing expected task cost under parameter uncertainty, and 2) minimizing optimality loss, which quantifies the degradation in task performance caused by planning with an incorrect parameter estimate. By actively optimizing for informative trajectories via a natural Fisher information measure, we tightly approach a lower bound on task-relevant parameter uncertainty while simultaneously achieving reliable task execution. Across diverse tasks, controllers, and adaptation laws, targeted exploration enables the identification required for successful task execution, allowing robots to learn relevant physical parameters while completing the task in a single attempt.

Abstract

Robotic Control

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