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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. 

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. 

Safe operations of autonomous mobile robots in close proximity to humans, creates a need for enhanced trajectory tracking (with low tracking errors). Linear optimal control techniques such as Linear Quadratic Regulator (LQR) and Model Predictive Control (MPC) have been used successfully for low-speed applications while leveraging their model-based methodology with manageable computational demands. However, model and parameter uncertainties or other unmodeled nonlinearities may cause poor control actions and constraint violations. Nonlinear MPC has emerged as an alternate optimal-control approach but needs to overcome real-time deployment challenges (including fast sampling time, design complexity, and limited computational resources). In recent years, the optimal control-based deployments have benefitted enormously from the ability of Deep Neural Networks (DNNs) to serve as universal function approximators. This has led to deployments in a plethora of previously inaccessible applications – but many aspects of generalizability, benchmarking, and systematic verification and validation coupled with benchmarking have emerged. This paper presents a novel approach to fusing Deep Reinforcement Learning-based (DRL) longitudinal control with a traditional PID lateral controller for autonomous navigation. Our approach follows (i) Generation of an adequate fidelity simulation scenario via a Real2Sim approach; (ii) training a DRL agent within this framework; (iii) Testing the performance and generalizability on alternate scenarios. We use an initial tuned set of the lateral PID controller gains for observing the vehicle response over a range of velocities. Then we use a DRL framework to generate policies for an optimal longitudinal controller that successfully complements the lateral PID to give the best tracking performance for the vehicle.