Task-Oriented Koopman-Based Control with Contrastive Encoder

We present task-oriented Koopman-based control that utilizes end-to-end reinforcement learning and contrastive encoder to simultaneously learn the Koopman latent embedding, operator and associated linear controller within an iterative loop. By prioritizing the task cost as main objective for controller learning, we reduce the reliance of controller design on a well-identified model, which extends Koopman control beyond low-dimensional systems to high-dimensional, complex nonlinear systems, including pixel-based scenarios.

Stability Bounds for Learning-Based Adaptive Control of Discrete-Time Multi-Dimensional Stochastic Linear Systems with Input Constraints

We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To address this challenge, we propose a certainty-equivalent control scheme which combines online parameter estimation with saturated linear control. We establish the existence of a high probability stability bound on the closed-loop system, under additional assumptions on the system and noise processes. Finally, numerical examples are presented to illustrate our results.

Knowledge Distillation for Feature Extraction in Underwater VSLAM

In recent years, learning-based feature detection and matching have outperformed manually-designed methods in in-air cases. However, it is challenging to learn the features in the underwater scenario due to the absence of annotated underwater datasets. This paper proposes a cross-modal knowledge distillation framework for training an underwater feature detection and matching network (UFEN). In particular, we use in-air RGBD data to generate synthetic underwater images based on a physical underwater imaging formation model and employ these as the medium to distil knowledge from a teacher model SuperPoint pretrained on in-air images. We embed UFEN into the ORB-SLAM3 framework to replace the ORB feature by introducing an additional binarization layer. To test the effectiveness of our method, we built a new underwater dataset with groundtruth measurements named EASI (https://github.com/Jinghe-mel/UFEN-SLAM), recorded in an indoor water tank for different turbidity levels. The experimental results on the existing dataset and our new dataset demonstrate the effectiveness of our method.

Learning-Based Adaptive Control for Stochastic Linear Systems with Input Constraints

We propose a certainty-equivalence scheme for adaptive control of scalar linear systems subject to additive, i.i.d. Gaussian disturbances and bounded control input constraints, without requiring prior knowledge of the bounds of the system parameters, nor the control direction. Assuming that the system is at-worst marginally stable, mean square boundedness of the closed-loop system states is proven. Lastly, numerical examples are presented to illustrate our results.

Data-driven Predictive Tracking Control based on Koopman Operators

We seek to combine the nonlinear modeling capabilities of a wide class of neural networks with the safety guarantees of model predictive control (MPC) in a rigorous and online computationally tractable framework. The class of networks considered can be captured using Koopman operators, and are integrated into a Koopman-based tracking MPC (KTMPC) for nonlinear systems to track piecewise constant references. The effect of model mismatch between original nonlinear dynamics and its trained Koopman linear model is handled by using a constraint tightening approach in the proposed tracking MPC strategy. By choosing two Lyapunov candidate functions, we prove that solution is recursively feasible and input-to-state stable to a neighborhood of both online and offline optimal reachable steady outputs in the presence of bounded modeling errors. Finally, we show the results of a numerical example and an application of autonomous ground vehicle to track given references.

Safety-guaranteed trajectory planning and control based on GP estimation for unmanned surface vessels

We propose a safety-guaranteed planning and control framework for unmanned surface vessels (USVs), using Gaussian processes (GPs) to learn uncertainties. The uncertainties encountered by USVs, including external disturbances and model mismatches, are potentially state-dependent, time-varying, and hard to capture with constant models. GP is a powerful learning-based tool that can be integrated with a model-based planning and control framework, which employs a Hamilton-Jacobi differential game formulation. Such a combination yields less conservative trajectories and safety-guaranteeing control strategies. We demonstrate the proposed framework in simulations and experiments on a CLEARPATH Heron USV.

FaSTrack: a Modular Framework for Real-Time Motion Planning and Guaranteed Safe Tracking

Real-time, guaranteed safe trajectory planning is vital for navigation in unknown environments. However, real-time navigation algorithms typically sacrifice robustness for computation speed. Alternatively, provably safe trajectory planning tends to be too computationally intensive for real-time replanning. We propose FaSTrack, Fast and Safe Tracking, a framework that achieves both real-time replanning and guaranteed safety. In this framework, real-time computation is achieved by allowing any trajectory planner to use a simplified \textit{planning model} of the system. The plan is tracked by the system, represented by a more realistic, higher-dimensional \textit{tracking model}. We precompute the tracking error bound (TEB) due to mismatch between the two models and due to external disturbances. We also obtain the corresponding tracking controller used to stay within the TEB. The precomputation does not require prior knowledge of the environment. We demonstrate FaSTrack using Hamilton-Jacobi reachability for precomputation and three different real-time trajectory planners with three different tracking-planning model pairs.

MBVI: Model-Based Value Initialization for Reinforcement Learning

Model-free reinforcement learning (RL) is capable of learning control policies for high-dimensional, complex robotic tasks, but tends to be data inefficient. Model-based RL and optimal control have been proven to be much more data-efficient if an accurate model of the system and environment is known, but can be difficult to scale to expressive models for high-dimensional problems. In this paper, we propose a novel approach to alleviate data inefficiency of model-free RL by warm-starting the learning process using model-based solutions. We do so by initializing a high-dimensional value function via supervision from a low-dimensional value function obtained by applying model-based techniques on a low-dimensional problem featuring an approximate system model. Therefore, our approach exploits the model priors from a simplified problem space implicitly and avoids the direct use of high-dimensional, expressive models. We demonstrate our approach on two representative robotic learning tasks and observe significant improvements in performance and efficiency, and analyze our method empirically with a third task.

A Sequential Approximation Framework for Coded Distributed Optimization

Building on the previous work of Lee et al. and Ferdinand et al. on coded computation, we propose a sequential approximation framework for solving optimization problems in a distributed manner. In a distributed computation system, latency caused by individual processors ("stragglers") usually causes a significant delay in the overall process. The proposed method is powered by a sequential computation scheme, which is designed specifically for systems with stragglers. This scheme has the desirable property that the user is guaranteed to receive useful (approximate) computation results whenever a processor finishes its subtask, even in the presence of uncertain latency. In this paper, we give a coding theorem for sequentially computing matrix-vector multiplications, and the optimality of this coding scheme is also established. As an application of the results, we demonstrate solving optimization problems using a sequential approximation approach, which accelerates the algorithm in a distributed system with stragglers.