Passive iFIR filters for data-driven velocity control in robotics

Yi Zhang; Zixing Wang; Fulvio Forni

cs.ROMar 31, 2026

Passive iFIR filters for data-driven velocity control in robotics

Authors: Yi Zhang, Zixing Wang, Fulvio Forni

Organizations: Department of Engineering, University of Cambridge, UK.

Abstract

We present a passive, data-driven velocity control method for nonlinear robotic manipulators that achieves better tracking performance than optimized PID with comparable design complexity. Using only three minutes of probing data, a VRFT-based design identifies passive iFIR controllers that (i) preserve closed-loop stability via passivity constraints and (ii) outperform a VRFT-tuned PID baseline on the Franka Research 3 robot in both joint-space and Cartesian-space velocity control, achieving up to a 74.5% reduction in tracking error for the Cartesian velocity tracking experiment with the most demanding reference model. When the robot end-effector dynamics change, the controller can be re-learned from new data, regaining nominal performance. This study bridges learning-based control and stability-guaranteed design: passive iFIR learns from data while retaining passivity-based stability guarantees, unlike many learning-based approaches.

Figures & tables

Panel of Figure 1 — Fig. 1 : Controlled robot velocity feedback loop with model reference in parallel. The output $y$ represents either single joint velocity or end-effector Cartesian velocity.

Panel of Figure 2 — Fig. 2 : A graphical interpretation of Theorem 1 .

Panel of Figure 3 — Fig. 3 : Single joint velocity control setting. Flexible wood strips of variable lengths are used to model different dynamic loads. Bode diagrams: reference model dynamics in black and (estimated, linearized) open-loop dynamics in blue .

Panel of Figure 4 — Fig. 4 : Joint space velocity tracking results. Black : target response and target reference model. Red : closed-loop response and sampled Bode diagram with iFIR controller. Blue : closed-loop response and sampled Bode diagram with PID controller.

	Step response (NRMSE)
	PID	iFIR	iFIR (without passivity constraint)	Improvement [%]
Nominal	0.156	0.092	–	41.0%
Dynamics change (without retraining)	0.146	0.105	–	28.1%
Dynamics change (with retraining)	0.093	0.096	–	-3.2%
Second order reference model	0.287	0.190	Instability	33.8%

TABLE I : Joint velocity control. The improvement is iFIR over PID. iFIR without passivity constraint was often unstable.

Panel of Figure 6 — Fig. 5 : Closed-loop response to sinusoidal reference (left) and step reference (right). Black : target response. Red : passive iFIR. Blue : PID. Gray : non-passive iFIR. Learning without passivity constraints can cause instability.

Panel of Figure 7 — Fig. 6 : Cartesian space velocity control results. Black : target response and target reference model. Red : closed-loop response and transfer function with iFIR controller. Blue : closed-loop response and transfer function with PID controller.

Controller type	Reference model	Random velocity profile (NRMSE)			Trapezoidal velocity profile (NRMSE)
Controller type	Reference model	PID	iFIR	Improvement [%]	PID	iFIR	Improvement [%]
SISO	$M_{r1}$	0.326	0.246	24.6%	0.113	0.091	19.7%
MIMO	$M_{r1}$	0.268	0.182	32.0%	0.119	0.096	19.2%
MIMO	$M_{r2}$	1.108	0.358	67.7%	0.660	0.169	74.5%

TABLE II : Performance summary for Cartesian space velocity control near the training configuration (random and trapezoidal velocity profiles). The improvement is iFIR over PID.

Fig. 7 : MIMO performance for

M_{r1}

: trapezoidal profile tracking when operating away from training configuration.

Robotic Control

Robotic control studies how machines use sensing and computation to produce reliable movement and interaction in changing environments.

See all 584 papers

L-Learning : A Lyapunov-Based Approach Leveraging Lagrangian Mechanics for Efficient and Stable Robot Tracking
May 26, 2026Quan Quan, Hao LiRobotic Control Robot Trajectory Tracking
1Quan Quan and Hao Li are with School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China
Robust Semi-passive Velocity Field Control with Boundedness Guarantees for Safe Interaction between Mechanical Systems and Physical Environment
Aug 31, 2026Van Trong Dang, Sumitaka Honji, Takahiro WadaSafety-Critical Control Robust Control
Graduate School of Science and Technology, Nara Institute of Science and Technology, Ikoma, Nara 630-0192, Japan
Lyapunov-Based PI-Like Control for Robust Trajectory Tracking of a Four-Wheel Independently Driven and Steered Robot: Design and Experimental Validation
Feb 17, 2026Branimir Ćaran, Vladimir Milić, Marko Švaco +1PID Control Robot Trajectory Tracking
Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb HR-10000, Croatia · Croatian Academy of Sciences and Arts, Zagreb 10000, Croatia

May 26, 2026J/K move · Enter open · S save

L-Learning : A Lyapunov-Based Approach Leveraging Lagrangian Mechanics for Efficient and Stable Robot Tracking

Quan Quan, Hao Li

1Quan Quan and Hao Li are with School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China

Robotic Control Robot Trajectory Tracking Lyapunov-Based Control Data-Driven Control

Open paper AskPDF arXiv

This paper presents L-Learning, a novel data-driven control framework for robotics that integrates Lyapunov stability theory with Lagrangian mechanics to enhance trajectory tracking performance. While traditional control methods often suffer from performance degradation in dynamic and uncertain environments, data-driven approaches, while more adaptable, are frequently limited by high sample complexity and a lack of rigorous stability guarantees. L-Learning mitigates these challenges by explicitly learning the system's energy function from data, thereby optimizing performance while ensuring closed-loop stability intrinsically. Characterized by superior control accuracy, theoretical stability guarantees, and high sample efficiency, L-Learning represents a promising solution for practical robotic applications.

Abstract

Robotic Control

Explore similar work

L-Learning : A Lyapunov-Based Approach Leveraging Lagrangian Mechanics for Efficient and Stable Robot Tracking

Robust Semi-passive Velocity Field Control with Boundedness Guarantees for Safe Interaction between Mechanical Systems and Physical Environment

Lyapunov-Based PI-Like Control for Robust Trajectory Tracking of a Four-Wheel Independently Driven and Steered Robot: Design and Experimental Validation