An official website of the United States government
The path-tracking control performance of an autonomous vehicle (AV) is crucially dependent upon modeling choices and subsequent system-identification updates. Traditionally, automotive engineering has built upon increasing fidelity of white- and gray-box models coupled with system identification. While these models offer explainability, they suffer from modeling inaccuracies, non-linearities, and parameter variation. On the other end, end-to-end black-box methods like behavior cloning and reinforcement learning provide increased adaptability but at the expense of explainability, generalizability, and the sim2real gap. In this regard, hybrid data-driven techniques like Koopman Extended Dynamic Mode Decomposition (KEDMD) can achieve linear embedding of non-linear dynamics through a selection of “lifting functions”. However, the success of this method is primarily predicated on the choice of lifting function(s) and optimization parameters. In this study, we present an analytical approach to construct these lifting functions using the iterative Lie bracket vector fields considering holonomic and non-holonomic constraints on the configuration manifold of our Ackermann-steered autonomous mobile robot. The prediction and control capabilities of the obtained linear KEDMD model are showcased using trajectory tracking of standard vehicle dynamics maneuvers and along a closed-loop racetrack.
more »
« less
Data-Driven Modeling and Experimental Validation of Autonomous Vehicles Using Koopman Operator
This paper presents a data-driven framework to discover underlying dynamics on a scaled F1TENTH vehicle using the Koopman operator linear predictor. Traditionally, a range of white, gray, or black-box models are used to develop controllers for vehicle path tracking. However, these models are constrained to either linearized operational domains, unable to handle significant variability or lose explainability through end-2-end operational settings. The Koopman Extended Dynamic Mode Decomposition (EDMD) linear predictor seeks to utilize data-driven model learning whilst providing benefits like explainability, model analysis and the ability to utilize linear model-based control techniques. Consider a trajectory-tracking problem for our scaled vehicle platform. We collect pose measurements of our F1TENTH car undergoing standard vehicle dynamics benchmark maneuvers with an OptiTrack indoor localization system. Utilizing these uniformly spaced temporal snapshots of the states and control inputs, a data-driven Koopman EDMD model is identified. This model serves as a linear predictor for state propagation, upon which an MPC feedback law is designed to enable trajectory tracking. The prediction and control capabilities of our framework are highlighted through real-time deployment on our scaled vehicle.
more »
« less
- PAR ID:
- 10490405
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- 2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
- ISBN:
- 978-1-6654-9190-7
- Page Range / eLocation ID:
- 9442 to 9447
- Format(s):
- Medium: X
- Location:
- Detroit, MI, USA
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Developing an accurate dynamic model for an Autonomous Underwater Vehicle (AUV) is challenging due to the diverse array of forces exerted on it in an underwater environment. These forces include hydrodynamic effects such as drag, buoyancy, and added mass. Consequently, achieving precision in predicting the AUV's behavior requires a comprehensive understanding of these dynamic forces and their interplay. In our research, we have devised a linear data-driven dynamic model rooted in Koopman's theory. The cornerstone of leveraging Koopman theory lies in accurately estimating the Koopman operator. To achieve this, we employ the dynamic mode decomposition (DMD) method, which enables the generation of the Koopman operator. We have developed a Fractional Sliding Mode Control (FSMC) method to provide robustness and high tracking performance for AUV systems. The efficacy of the proposed controller has been verified through simulation results.more » « less
-
null (Ed.)This paper presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms of the prediction horizon and the magnitude of the derivatives of the system states. Using higher order derivatives of general nonlinear dynamics that need not be known, we construct a Koopman operator-based linear representation and utilize Taylor series accuracy analysis to derive an error bound. The resulting error formula is used to choose the order of derivatives in the basis functions and obtain a data-driven Koopman model using a closed-form expression that can be computed in real time. Using the inverted pendulum system, we illustrate the robustness of the error bounds given noisy measurements of unknown dynamics, where the derivatives are estimated numerically. When combined with control, the Koopman representation of the nonlinear system has marginally better performance than competing nonlinear modeling methods, such as SINDy and NARX. In addition, as a linear model, the Koopman approach lends itself readily to efficient control design tools, such as LQR, whereas the other modeling approaches require nonlinear control methods. The efficacy of the approach is further demonstrated with simulation and experimental results on the control of a tail-actuated robotic fish. Experimental results show that the proposed data-driven control approach outperforms a tuned PID (Proportional Integral Derivative) controller and that updating the data-driven model online significantly improves performance in the presence of unmodeled fluid disturbance. This paper is complemented with a video: https://youtu.be/9 wx0tdDta0.more » « less
-
This research proposes a new fractional robust data-driven control method to control a nonlinear dynamic micro-electromechanical (MEMS) gyroscope model. The Koopman theory is used to linearize the nonlinear dynamic model of MEMS gyroscope, and the Koopman operator is obtained by using the dynamic mode decomposition (DMD) method. However, external disturbances constantly affect the MEMS gyroscope. To compensate for these perturbations, a fractional sliding mode controller (FOSMC) is applied. The FOSMC has several advantages, including high trajectory tracking performance and robustness. However, one of the drawbacks of FOSMC is generating high control inputs. To overcome this limitation, the researchers proposed a compound controller design that applies fractional proportional integral derivative (FOPID) to reduce the control efforts. The simulation results showed that the proposed compound Koopman-FOSMC and FOPID (Koopman-CFOPIDSMC) outperformed two other controllers, including FOSMC and Koopman-FOSMC, in terms of performance. Therefore, this research proposes an effective approach to control the nonlinear dynamic model of MEMS gyroscope.more » « less
-
Cable driven parallel robots (CDPRs) are often challenging to model and to dynamically control due to the inherent flexibility and elasticity of the cables. The additional inclusion of online geometric reconfigurability to a CDPR results in a complex underdetermined system with highly non-linear dynamics. The necessary (numerical) redundancy resolution requires multiple layers of optimization rendering its application computationally prohibitive for real-time control. Here, deep reinforcement learning approaches can offer a model-free framework to overcome these challenges and can provide a real-time capable dynamic control. This study discusses three settings for a model-free DRL implementation in dynamic trajectory tracking: (i) for a standard non-redundant CDPR with a fixed workspace; (ii) in an end-to-end setting with redundancy resolution on a reconfigurable CDPR; and (iii) in a decoupled approach resolving kinematic and actuation redundancies individually.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/IROS55552.2023.10341797
