arXiv subjects

Ivan Dario Jimenez Rodriguez

Publications and source records attributed to Ivan Dario Jimenez Rodriguez.

9 recordsLinked to original sources

arXiv2025

KALIKO: Kalman-Implicit Koopman Operator Learning For Prediction of Nonlinear Dynamical Systems

Long-horizon dynamical prediction is fundamental in robotics and control, underpinning canonical methods like model predictive control. Yet, many systems and disturbance phenomena are difficult to model due to effects like nonlinearity, chaos, and high-dimensionality. Koopman theory addresses this by modeling the linear evolution of embeddings of the state under an infinite-dimensional linear operator that can be approximated with a suitable finite basis of embedding functions, effectively trading model nonlinearity for representational complexity. However, explicitly computing a good choice of basis is nontrivial, and poor choices may cause inaccurate forecasts or overfitting. To address this, we present Kalman-Implicit Koopman Operator (KALIKO) Learning, a method that leverages the Kalman filter to implicitly learn embeddings corresponding to latent dynamics without requiring an explicit encoder. KALIKO produces interpretable representations consistent with both theory and prior works, yielding high-quality reconstructions and inducing a globally linear latent dynamics. Evaluated on wave data generated by a high-dimensional PDE, KALIKO surpasses several baselines in open-loop prediction and in a demanding closed-loop simulated control task: stabilizing an underactuated manipulator's payload by predicting and compensating for strong wave disturbances.

cs.RO↗

arXiv2024

Robust Agility via Learned Zero Dynamics Policies

We study the design of robust and agile controllers for hybrid underactuated systems. Our approach breaks down the task of creating a stabilizing controller into: 1) learning a mapping that is invariant under optimal control, and 2) driving the actuated coordinates to the output of that mapping. This approach, termed Zero Dynamics Policies, exploits the structure of underactuation by restricting the inputs of the target mapping to the subset of degrees of freedom that cannot be directly actuated, thereby achieving significant dimension reduction. Furthermore, we retain the stability and constraint satisfaction of optimal control while reducing the online computational overhead. We prove that controllers of this type stabilize hybrid underactuated systems and experimentally validate our approach on the 3D hopping platform, ARCHER. Over the course of 3000 hops the proposed framework demonstrates robust agility, maintaining stable hopping while rejecting disturbances on rough terrain.

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arXiv2024

Constructive Nonlinear Control of Underactuated Systems via Zero Dynamics Policies

Stabilizing underactuated systems is an inherently challenging control task due to fundamental limitations on how the control input affects the unactuated dynamics. Decomposing the system into actuated (output) and unactuated (zero) coordinates provides useful insight as to how input enters the system dynamics. In this work, we leverage the structure of this decomposition to formalize the idea of Zero Dynamics Policies (ZDPs) -- a mapping from the unactuated coordinates to desired actuated coordinates. Specifically, we show that a ZDP exists in a neighborhood of the origin, and prove that combining output stabilization with a ZDP results in stability of the full system state. We detail a constructive method of obtaining ZDPs in a neighborhood of the origin, and propose a learning-based approach which leverages optimal control to obtain ZDPs with much larger regions of attraction. We demonstrate that such a paradigm can be used to stabilize the canonical underactuated system of the cartpole, and showcase an improvement over the nominal performance of LQR.

eess.SY↗

arXiv2023

FI-ODE: Certifiably Robust Forward Invariance in Neural ODEs

Forward invariance is a long-studied property in control theory that is used to certify that a dynamical system stays within some pre-specified set of states for all time, and also admits robustness guarantees (e.g., the certificate holds under perturbations). We propose a general framework for training and provably certifying robust forward invariance in Neural ODEs. We apply this framework to provide certified safety in robust continuous control. To our knowledge, this is the first instance of training Neural ODE policies with such non-vacuous certified guarantees. In addition, we explore the generality of our framework by using it to certify adversarial robustness for image classification.

cs.LG↗

arXiv2022

Safe Drone Flight with Time-Varying Backup Controllers

The weight, space, and power limitations of small aerial vehicles often prevent the application of modern control techniques without significant model simplifications. Moreover, high-speed agile behavior, such as that exhibited in drone racing, make these simplified models too unreliable for safety-critical control. In this work, we introduce the concept of time-varying backup controllers (TBCs): user-specified maneuvers combined with backup controllers that generate reference trajectories which guarantee the safety of nonlinear systems. TBCs reduce conservatism when compared to traditional backup controllers and can be directly applied to multi-agent coordination to guarantee safety. Theoretically, we provide conditions under which TBCs strictly reduce conservatism, describe how to switch between several TBC's and show how to embed TBCs in a multi-agent setting. Experimentally, we verify that TBCs safely increase operational freedom when filtering a pilot's actions and demonstrate robustness and computational efficiency when applied to decentralized safety filtering of two quadrotors.

eess.SY↗

arXiv2022

Neural Gaits: Learning Bipedal Locomotion via Control Barrier Functions and Zero Dynamics Policies

This work presents Neural Gaits, a method for learning dynamic walking gaits through the enforcement of set invariance that can be refined episodically using experimental data from the robot. We frame walking as a set invariance problem enforceable via control barrier functions (CBFs) defined on the reduced-order dynamics quantifying the underactuated component of the robot: the zero dynamics. Our approach contains two learning modules: one for learning a policy that satisfies the CBF condition, and another for learning a residual dynamics model to refine imperfections of the nominal model. Importantly, learning only over the zero dynamics significantly reduces the dimensionality of the learning problem while using CBFs allows us to still make guarantees for the full-order system. The method is demonstrated experimentally on an underactuated bipedal robot, where we are able to show agile and dynamic locomotion, even with partially unknown dynamics.

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arXiv2022

LyaNet: A Lyapunov Framework for Training Neural ODEs

We propose a method for training ordinary differential equations by using a control-theoretic Lyapunov condition for stability. Our approach, called LyaNet, is based on a novel Lyapunov loss formulation that encourages the inference dynamics to converge quickly to the correct prediction. Theoretically, we show that minimizing Lyapunov loss guarantees exponential convergence to the correct solution and enables a novel robustness guarantee. We also provide practical algorithms, including one that avoids the cost of backpropagating through a solver or using the adjoint method. Relative to standard Neural ODE training, we empirically find that LyaNet can offer improved prediction performance, faster convergence of inference dynamics, and improved adversarial robustness. Our code available at https://github.com/ivandariojr/LyapunovLearning .

cs.LG↗

arXiv2020

Optimization Methods for Interpretable Differentiable Decision Trees in Reinforcement Learning

Decision trees are ubiquitous in machine learning for their ease of use and interpretability. Yet, these models are not typically employed in reinforcement learning as they cannot be updated online via stochastic gradient descent. We overcome this limitation by allowing for a gradient update over the entire tree that improves sample complexity affords interpretable policy extraction. First, we include theoretical motivation on the need for policy-gradient learning by examining the properties of gradient descent over differentiable decision trees. Second, we demonstrate that our approach equals or outperforms a neural network on all domains and can learn discrete decision trees online with average rewards up to 7x higher than a batch-trained decision tree. Third, we conduct a user study to quantify the interpretability of a decision tree, rule list, and a neural network with statistically significant results ($p < 0.001$).

cs.LG↗

arXiv2019

Differentiable MPC for End-to-end Planning and Control

We present foundations for using Model Predictive Control (MPC) as a differentiable policy class for reinforcement learning in continuous state and action spaces. This provides one way of leveraging and combining the advantages of model-free and model-based approaches. Specifically, we differentiate through MPC by using the KKT conditions of the convex approximation at a fixed point of the controller. Using this strategy, we are able to learn the cost and dynamics of a controller via end-to-end learning. Our experiments focus on imitation learning in the pendulum and cartpole domains, where we learn the cost and dynamics terms of an MPC policy class. We show that our MPC policies are significantly more data-efficient than a generic neural network and that our method is superior to traditional system identification in a setting where the expert is unrealizable.

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