Stability certificates play a critical role in ensuring the safety and reliability of robotic systems. However, deriving these certificates for complex, unknown systems has traditionally required explicit knowledge of system dynamics, often making it a daunting task. This work introduces a novel framework that learns a Lyapunov function directly from trajectory data, enabling the certification of stability for autonomous systems without needing detailed system models. By parameterizing the Lyapunov candidate using a neural network and ensuring positive definiteness through Cholesky factorization, our approach automatically identifies whether the system is stable under the given trajectory. To address the challenges posed by noisy, real-world data, we allow for controlled violations of the stability condition, focusing on maintaining high confidence in the stability certification process. Our results demonstrate that this framework can provide data-driven stability guarantees, offering a robust method for certifying the safety of robotic systems in dynamic, real-world environments. This approach works without access to the internal control algorithms, making it applicable even in situations where system behavior is opaque or proprietary. The tool for learning the stability proof is open-sourced by this research: https://github.com/HansOersted/stability.

This paper presents a framework for enabling safe velocity control of general robotic systems using data-driven model-free Control Barrier Functions (CBFs). Model-free CBFs rely on an exponentially stable velocity controller and a design parameter (e.g. alpha in CBFs); this design parameter depends on the exponential decay rate of the controller. However, in practice, the decay rate is often unavailable, making it non-trivial to use model-free CBFs, as it requires manual tuning for alpha. To address this, a Neural Network is used to learn the Lyapunov function from data, and the maximum decay rate of the systems built-in velocity controller is subsequently estimated. Furthermore, to integrate the estimated decay rate with model-free CBFs, we derive a probabilistic safety condition that incorporates a confidence bound on the violation rate of the exponential stability condition, using Chernoff bound. This enhances robustness against uncertainties in stability violations. The proposed framework has been tested on a UR5e robot in multiple experimental settings, and its effectiveness in ensuring safe velocity control with model-free CBFs has been demonstrated.

Gradient based optimization algorithms deployed in Machine Learning (ML) applications are often analyzed and compared by their convergence rates or regret bounds. While these rates and bounds convey valuable information they don't always directly translate to stability guarantees. Stability and similar concepts, like robustness, will become ever more important as we move towards deploying models in real-time and safety critical systems. In this work we build upon the results in Gaudio et al. 2021 and Moreu and Annaswamy 2022 for second order gradient descent when applied to explicitly time varying cost functions and provide more general stability guarantees. These more general results can aid in the design and certification of these optimization schemes so as to help ensure safe and reliable deployment for real-time learning applications. We also hope that the techniques provided here will stimulate and cross-fertilize the analysis that occurs on the same algorithms from the online learning and stochastic optimization communities.

Imitation learning is a paradigm to address complex motion planning problems by learning a policy to imitate an expert's behavior. However, relying solely on the expert's data might lead to unsafe actions when the robot deviates from the demonstrated trajectories. Stability guarantees have previously been provided utilizing nonlinear dynamical systems, acting as high-level motion planners, in conjunction with the Lyapunov stability theorem. Yet, these methods are prone to inaccurate policies, high computational cost, sample inefficiency, or quasi stability when replicating complex and highly nonlinear trajectories. To mitigate this problem, we present an approach for learning a globally stable nonlinear dynamical system as a motion planning policy. We model the nonlinear dynamical system as a parametric polynomial and learn the polynomial's coefficients jointly with a Lyapunov candidate. To showcase its success, we compare our method against the state of the art in simulation and conduct real-world experiments with the Kinova Gen3 Lite manipulator arm. Our experiments demonstrate the sample efficiency and reproduction accuracy of our method for various expert trajectories, while remaining stable in the face of perturbations.

Recent quadrotors have transcended conventional designs, emphasizing more on foldable and reconfigurable bodies. The state of the art still focuses on the mechanical feasibility of such designs with limited discussions on the tracking performance of the vehicle during configuration switching. In this article, we first present a common framework to analyse the attitude errors of a folding quadrotor via the theory of switched systems. We then employ this framework to investigate the attitude tracking performance for two case scenarios - one with a conventional geometric controller for precisely known system dynamics; and second, with our proposed morphology-aware adaptive controller that accounts for any modeling uncertainties and disturbances. Finally, we cater to the desired switching requirements from our stability analysis by exploiting the trajectory planner to obtain superior tracking performance while switching. Simulation results are presented that validate the proposed control and planning framework for a foldable quadrotor's flight through a passageway.

Since batch algorithms suffer from lack of proficiency in confronting model mismatches and disturbances, this contribution proposes an adaptive scheme based on continuous Lyapunov function for online robot dynamic identification. This paper suggests stable updating rules to drive neural networks inspiring from model reference adaptive paradigm. Network structure consists of three parallel self-driving neural networks which aim to estimate robot dynamic terms individually. Lyapunov candidate is selected to construct energy surface for a convex optimization framework. Learning rules are driven directly from Lyapunov functions to make the derivative negative. Finally, experimental results on 3-DOF Phantom Omni Haptic device demonstrate efficiency of the proposed method.