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
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.
Fig. 2 : A graphical interpretation of Theorem 1 .
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 .
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.
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.
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)
PID
iFIR
Improvement [%]
PID
iFIR
Improvement [%]
SISO
Mr1
0.326
0.246
24.6%
0.113
0.091
19.7%
MIMO
Mr1
0.268
0.182
32.0%
0.119
0.096
19.2%
MIMO
Mr2
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 Mr1 : trapezoidal profile tracking when operating away from training configuration.
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.
Quan Quan, Hao Li
1Quan Quan and Hao Li are with School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China
Controllers that guarantee energetic passivity with respect to the pair of external force and velocity realize safe interaction between the mechanical system and its physical environment. However, solely adhering to energetic passivity constraints may impose fundamental limitations on control performance and, in some cases, prevent the successful execution of controlled tasks. In addition, external disturbances from the physical environment can drive the system energy level and states beyond operational regions, thereby undermining task performance and safety. In this paper, we study a robust time-varying semi-passive velocity field control to aim to relax the inherently conservative nature of fully passive control methods in a controlled manner. Specifically, the proposed control method guarantees passivity of the closed-loop system with respect to the force-velocity input-output pair when the energy level exceeds a predefined level, while permitting non-passive behaviors to preserve task performance otherwise. Furthermore, the energy level and the states of the closed-loop system are proved to converge to bounded domains even in the presence of unpredicted disturbances. Additionally, the proposed method also enables constraining power flow between the closed-loop system and its physical environment to enhance safety in the interaction process. Numerical simulation examples demonstrate the effectiveness of the proposed method.
Van Trong Dang, Sumitaka Honji, Takahiro Wada
Graduate School of Science and Technology, Nara Institute of Science and Technology, Ikoma, Nara 630-0192, Japan
In this paper, a Lyapunov-based synthesis of a PI-like controller is proposed for robust trajectory tracking of an independently driven and steered four-wheel mobile robot. For the robot considered in this work, an explicit structurally verified mathematical model is used to enable systematic controller design with rigorous stability guarantees suitable for real time implementation. An augmented Lyapunov-based practical stability analysis is developed for the combined velocity-error and integral-error dynamics of the inner loop, yielding explicit bounds and sufficient conditions for practical stability and uniform ultimate boundedness of the combined velocity-error and integral-error state. The resulting control law retains a PI-like structure with model-based feedforward compensation, making it suitable for implementation on standard embedded platforms while improving robustness against configuration dependent residual dynamics and unmodelled effects. The effectiveness and robustness of the proposed design are demonstrated experimentally on a four-wheel independently steered and independently driven mobile robot platform, under both horizontal and vertical operating conditions and benchmarked against a PI controller and a sliding-mode controller.
Branimir Ćaran, Vladimir Milić, Marko Švaco +1
Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb HR-10000, Croatia · Croatian Academy of Sciences and Arts, Zagreb 10000, Croatia