Zehui Lu

Wenjian Hao, Zehui Lu, Devesh Upadhyay et al.

This paper proposes a distributed data-driven framework for dynamics learning, termed distributed deep Koopman learning using partial trajectories (DDKL-PT). In this framework, each agent in a multi-agent system is assigned a partial trajectory offline and locally approximates the unknown dynamics using a deep neural network within the Koopman operator framework. By exchanging local estimated dynamics rather than training data, agents achieve consensus on a global dynamics model without sharing their private training trajectories. Simulation studies on a surface vehicle demonstrate that DDKL-PT achieves consensus on the learned dynamics, and each agent attains reasonably small approximation errors on the testing dataset. Furthermore, a model predictive control scheme is developed by integrating the learned Koopman dynamics with known kinematic relations. Results on a reference-tracking task indicate that the distributedly learned dynamics are sufficiently accurate for model-based optimal control.

Wenjian Hao, Yuxuan Fang, Zehui Lu et al.

This paper presents a model-based reinforcement learning (RL) framework for optimal closed-loop control of nonlinear robotic systems. The proposed approach learns linear lifted dynamics through Koopman operator theory and integrates the resulting model into an actor-critic architecture for policy optimization, where the policy represents a parameterized closed-loop controller. To reduce computational cost and mitigate model rollout errors, policy gradients are estimated using one-step predictions of the learned dynamics rather than multi-step propagation. This leads to an online mini-batch policy gradient framework that enables policy improvement from streamed interaction data. The proposed framework is evaluated on several simulated nonlinear control benchmarks and two real-world hardware platforms, including a Kinova Gen3 robotic arm and a Unitree Go1 quadruped. Experimental results demonstrate improved sample efficiency over model-free RL baselines, superior control performance relative to model-based RL baselines, and control performance comparable to classical model-based methods that rely on exact system dynamics.

Tianyu Zhou, Zihao Liang, Zehui Lu et al.

This paper presents an online intention prediction framework for estimating the goal state of autonomous systems in real time, even when intention is time-varying, and system dynamics or objectives include unknown parameters. The problem is formulated as an inverse optimal control / inverse reinforcement learning task, with the intention treated as a parameter in the objective. A shifting horizon strategy discounts outdated information, while online control-informed learning enables efficient gradient computation and online parameter updates. Simulations under varying noise levels and hardware experiments on a quadrotor drone demonstrate that the proposed approach achieves accurate, adaptive intention prediction in complex environments.

Tianyu Zhou, Zihao Liang, Zehui Lu et al.

This paper proposes a Safe Online Control-Informed Learning framework for safety-critical autonomous systems. The framework unifies optimal control, parameter estimation, and safety constraints into an online learning process. It employs an extended Kalman filter to incrementally update system parameters in real time, enabling robust and data-efficient adaptation under uncertainty. A softplus barrier function enforces constraint satisfaction during learning and control while eliminating the dependence on high-quality initial guesses. Theoretical analysis establishes convergence and safety guarantees, and the framework's effectiveness is demonstrated on cart-pole and robot-arm systems.

Wenjian Hao, Zehui Lu, Zihao Liang et al.

This paper develops a policy learning method for tuning a pre-trained policy to adapt to additional tasks without altering the original task. A method named Adaptive Policy Gradient (APG) is proposed in this paper, which combines Bellman's principle of optimality with the policy gradient approach to improve the convergence rate. This paper provides theoretical analysis which guarantees the convergence rate and sample complexity of $\mathcal{O}(1/T)$ and $\mathcal{O}(1/ε)$, respectively, where $T$ denotes the number of iterations and $ε$ denotes the accuracy of the resulting stationary policy. Furthermore, several challenging numerical simulations, including cartpole, lunar lander, and robot arm, are provided to show that APG obtains similar performance compared to existing deterministic policy gradient methods while utilizing much less data and converging at a faster rate.

Wanxin Jin, Todd D. Murphey, Zehui Lu et al.

This paper proposes a novel approach that enables a robot to learn an objective function incrementally from human directional corrections. Existing methods learn from human magnitude corrections; since a human needs to carefully choose the magnitude of each correction, those methods can easily lead to over-corrections and learning inefficiency. The proposed method only requires human directional corrections -- corrections that only indicate the direction of an input change without indicating its magnitude. We only assume that each correction, regardless of its magnitude, points in a direction that improves the robot's current motion relative to an unknown objective function. The allowable corrections satisfying this assumption account for half of the input space, as opposed to the magnitude corrections which have to lie in a shrinking level set. For each directional correction, the proposed method updates the estimate of the objective function based on a cutting plane method, which has a geometric interpretation. We have established theoretical results to show the convergence of the learning process. The proposed method has been tested in numerical examples, a user study on two human-robot games, and a real-world quadrotor experiment. The results confirm the convergence of the proposed method and further show that the method is significantly more effective (higher success rate), efficient/effortless (less human corrections needed), and potentially more accessible (fewer early wasted trials) than the state-of-the-art robot learning frameworks.