arXiv subjects

Rodrigo Aldana-López

Publications and source records attributed to Rodrigo Aldana-López.

At least 19 recordsLinked to original sources

arXiv2026

Abstract homogeneous chains: a Lyapunov framework for high-order sliding modes in multi-agent systems

This work develops a Lyapunov framework for a broad class of arbitrary-order sliding-mode algorithms in multi-agent systems. We introduce abstract homogeneous chains, a class of nonlinear error systems characterized by common convexity and homogeneity properties. For this class, we establish global finite-time stability for arbitrary order, construct a homogeneous Lyapunov function, and derive a recursive optimization-based gain-proposal procedure. The framework addresses several gaps in existing dynamic average consensus and distributed differentiation results: it provides a recursive numerical optimization-based gain-proposal procedure for EDCHO at arbitrary order, extends REDCHO convergence from local to global, and provides arbitrary-order numerical gain-proposal rules for leader-follower distributed differentiation, previously available only at first order. It also provides a new arbitrary-order observer for multi-leader affine formation tracking with global finite-time convergence.

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arXiv2026

Event-triggered parameter estimator for sensor fusion

This paper studies event-triggered parameter estimation in sensor fusion systems where sensors transmit measurements to a gradient based estimator. We introduce a regressor-driven local triggering rule that requires no knowledge of the current parameter estimate and depends solely on the regressor signals. Under a persistent excitation condition on the aggregate regressor, we derive explicit design inequalities on the estimator gain and event thresholds that guarantee global exponential convergence. The analysis is based on a time-varying Lyapunov function. We further provide a sufficient condition on the regressor dynamics that enforces a uniform lower bound on inter-event times, excluding Zeno behavior. Simulations show substantial communication savings while preserving exponential convergence.

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arXiv2026

Autonomous and non-autonomous fixed-time leader-follower consensus for second-order multi-agent systems

This paper addresses the problem of consensus tracking with fixed-time convergence, for leader-follower multi-agent systems with double-integrator dynamics, where only a subset of followers has access to the state of the leader. The control scheme is divided into two steps. The first one is dedicated to the estimation of the leader state by each follower in a distributed way and in a fixed-time. Then, based on the estimate of the leader state, each follower computes its control law to track the leader in a fixed-time. In this paper, two control strategies are investigated and compared to solve the two mentioned steps. The first one is an autonomous protocol which ensures a fixed-time convergence for the observer and for the controller parts where the Upper Bound of the Settling-Time (UBST) is set a priory by the user. Then, the previous strategy is redesigned using time-varying gains to obtain a non-autonomous protocol. This enables to obtain less conservative estimates of the UBST while guaranteeing that the time-varying gains remain bounded. Some numerical examples show the effectiveness of the proposed consensus protocols.

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arXiv2026

Super-twisting over networks: A Lyapunov approach for distributed differentiation

We study distributed differentiation, where agents in a networked system estimate the average of local time-varying signals and their derivatives under mild assumptions on the agents' signals and their first and second derivatives. Existing sliding-mode methods provide only local stability guarantees and lack systematic gain selection. By isolating the structural features shared with the super-twisting algorithm and encoding them into an abstract model, we construct a Lyapunov function enabling systematic gain design and proving global finite-time convergence to consensus for the distributed differentiator. Building on this framework, we develop an event-triggered hybrid system implementation using time-varying and state dependent threshold rules and derive minimum inter-event time guarantees and accuracy bounds that quantify the trade-off between estimation accuracy and communication effort.

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arXiv2025

Distributed Discrete-time Dynamic Outer Approximation of the Intersection of Ellipsoids

This paper presents the first discrete-time distributed algorithm to track the tightest ellipsoids that outer approximates the global dynamic intersection of ellipsoids. Given an undirected network, we consider a setup where each node measures an ellipsoid, defined as a time-varying positive semidefinite matrix. The goal is to devise a distributed algorithm to track the tightest outer approximation of the intersection of all the ellipsoids. The solution is based on a novel distributed reformulation of the original centralized semi-definite outer Löwner-John program, characterized by a non-separable objective function and global constraints. We prove finite-time convergence to the global minima of the centralized problem in the static case and finite-time bounded tracking error in the dynamic case. Moreover, we prove boundedness of estimation in the tracking of the global optimum and robustness in the estimation against time-varying inputs. We illustrate the properties of the algorithm with different simulated examples, including a distributed estimation showcase where our proposal is integrated into a distributed Kalman filter to surpass the state-of-the-art in mean square error performance.

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arXiv2024

Towards Parameter-free Distributed Optimization: a Port-Hamiltonian Approach

This paper introduces a novel distributed optimization technique for networked systems, which removes the dependency on specific parameter choices, notably the learning rate. Traditional parameter selection strategies in distributed optimization often lead to conservative performance, characterized by slow convergence or even divergence if parameters are not properly chosen. In this work, we propose a systems theory tool based on the port-Hamiltonian formalism to design algorithms for consensus optimization programs. Moreover, we propose the Mixed Implicit Discretization (MID), which transforms the continuous-time port-Hamiltonian system into a discrete time one, maintaining the same convergence properties regardless of the step size parameter. The consensus optimization algorithm enhances the convergence speed without worrying about the relationship between parameters and stability. Numerical experiments demonstrate the method's superior performance in convergence speed, outperforming other methods, especially in scenarios where conventional methods fail due to step size parameter limitations.

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arXiv2024

Latency vs precision: Stability preserving perception scheduling

In robotic systems, perception latency is a term that refers to the computing time measured from the data acquisition to the moment in which perception output is ready to be used to compute control commands. There is a compromise between perception latency, precision for the overall robotic system, and computational resource usage referred to here as the latency-precision trade-off. In this work, we analyze a robot model given by a linear system, a zero-order hold controller, and measurements taken by several perception mode possibilities with different noise levels. We show that the analysis of this system is reduced to studying an equivalent switching system. Our goal is to schedule perception modes such that stability is attained while optimizing a cost function that models the latency-precision trade-off. Our solution framework comprises three main tools: the construction of perception scheduling policy candidates, admissibility verification for policy candidates, and optimal strategies based on admissible policies.

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arXiv2024

Perception-latency aware distributed target tracking

This work is devoted to the problem of distributed target tracking when a team of robots detect the target through a variable perception-latency mechanism. A reference for the robots to track is constructed in terms of a desired formation around the estimation of the target position. However, it is noted that due to the perception-latency, classical estimation techniques have smoothness issues which prevent asymptotic stability for the formation control. We propose a near-optimal smooth-output estimator which circumvents this issue. Moreover, local estimations are fused using novel dynamic consensus techniques. The advantages of the proposal as well as a comparison with a non-smooth optimal alternative are discussed through simulation examples.

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arXiv2024

PLATE: A perception-latency aware estimator,

Target tracking is a popular problem with many potential applications. There has been a lot of effort on improving the quality of the detection of targets using cameras through different techniques. In general, with higher computational effort applied, i.e., a longer perception-latency, a better detection accuracy is obtained. However, it is not always useful to apply the longest perception-latency allowed, particularly when the environment doesn't require to and when the computational resources are shared between other tasks. In this work, we propose a new Perception-LATency aware Estimator (PLATE), which uses different perception configurations in different moments of time in order to optimize a certain performance measure. This measure takes into account a perception-latency and accuracy trade-off aiming for a good compromise between quality and resource usage. Compared to other heuristic frame-skipping techniques, PLATE comes with a formal complexity and optimality analysis. The advantages of PLATE are verified by several experiments including an evaluation over a standard benchmark with real data and using state of the art deep learning object detection methods for the perception stage.

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arXiv2023

On inherent limitations in robustness and performance for a class of prescribed-time algorithms

Prescribed-time algorithms based on time-varying gains may have remarkable properties, such as regulation in a user-prescribed finite time that is the same for every nonzero initial condition and that holds even under matched disturbances. However, at the same time, such algorithms are known to lack robustness to measurement noise. This note shows that the lack of robustness of a class of prescribed-time algorithms is of an extreme form. Specifically, we show the existence of arbitrarily small measurement noises causing considerable deviations, divergence, and other detrimental consequences. We also discuss some drawbacks and trade-offs of existing workarounds as motivation for further analysis.

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arXiv2023

Designing controllers with predefined convergence-time bound using bounded time-varying gains

Recently, there has been a great deal of attention in a class of controllers based on time-varying gains, called prescribed-time controllers, that steer the system's state to the origin in the desired time, a priori set by the user, regardless of the initial condition. Furthermore, such a class of controllers has been shown to maintain a prescribed-time convergence in the presence of disturbances even if the disturbance bound is unknown. However, such properties require a time-varying gain that becomes singular at the terminal time, which limits its application to scenarios under quantization or measurement noise. This chapter presents a methodology to design a broader class of controllers, called predefined-time controllers, with a prescribed convergence-time bound. Our approach allows designing robust predefined-time controllers based on time-varying gains while maintaining uniformly bounded time-varying gains. We analyze the condition for uniform Lyapunov stability under the proposed time-varying controllers.

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arXiv2023

An arbitrary-order predefined-time exact differentiator for signals with exponential growth bound

There is a growing interest in differentiation algorithms that converge in fixed time with a predefined Upper Bound on the Settling Time (UBST). However, existing differentiation algorithms are limited to signals having an $n$-th order Lipschitz derivative. Here, we introduce a general methodology based on time-varying gains to circumvent this limitation, allowing us to design $n$-th order differentiators with a predefined UBST for the broader class of signals whose $(n+1)$-th derivative is bounded by a function with bounded logarithmic derivative. Unlike existing methods whose time-varying gain tends to infinity, our approach yields a time-varying gain that remains bounded at convergence time. We show how this last property maintains exact convergence using bounded gains when considering a compact set of initial conditions and improves the algorithm's performance to measurement noise.

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arXiv2022

Designing predefined-time differentiators with bounded time-varying gains

There is an increasing interest in designing differentiators, which converge exactly before a prespecified time regardless of the initial conditions, i.e., which are fixed-time convergent with a predefined Upper Bound of their Settling Time (UBST), due to their ability to solve estimation and control problems with time constraints. However, for the class of signals with a known bound of their $(n+1)$-th time derivative, the existing design methodologies yield a very conservative UBST, or result in gains that tend to infinity at the convergence time. Here, we introduce a new methodology based on time-varying gains to design arbitrary-order exact differentiators with a predefined UBST. This UBST is a priori set as one parameter of the algorithm. Our approach guarantees that the UBST can be set arbitrarily tight, and we also provide sufficient conditions to obtain exact convergence while maintaining bounded time-varying gains. Additionally, we provide necessary and sufficient conditions such that our approach yields error dynamics with a uniformly Lyapunov stable equilibrium. Our results show how time-varying gains offer a general and flexible methodology to design algorithms with a predefined UBST.

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arXiv2022

Dynamic consensus with prescribed convergence time for multi-leader formation tracking

This work addresses the problem of distributed formation tracking for a group of follower holonomic mobile robots around a reference signal. The reference signal is comprised of the geometric center of the positions of multiple leaders. This work's main contribution is a novel Modulated Distributed Virtual Observer (MDVO) for the reference signal. Moreover, the proposed MDVO is based on an exact dynamic consensus algorithm with a prescribed convergence time. In addition, we provide simulation examples showcasing two different application scenarios for the proposal.

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arXiv2022

EDCHO: High Order Exact Dynamic Consensus

This article addresses the problem of average consensus in a multi-agent system when the desired consensus quantity is a time varying signal. Although this problem has been addressed in existing literature by linear schemes, only bounded steady-state errors have been achieved. Other approaches have used first order sliding modes to achieve zero steady-state error, but suffer from the chattering effect. In this work, we propose a new exact dynamic consensus algorithm which leverages high order sliding modes, in the form of a distributed differentiator to achieve zero steady-state error of the average of time varying reference signals in a group of agents. Moreover, our proposal is also able to achieve consensus to high order derivatives of the average signal, if desired. An in depth formal study on the stability and convergence for EDCHO is provided for undirected connected graphs. Finally, the effectiveness and advantages of our proposal are shown with concrete simulation scenarios.

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arXiv2022

REDCHO: Robust Exact Dynamic Consensus of High Order

This article addresses the problem of average consensus in a multi-agent system when the desired consensus quantity is a time varying signal. Recently, the EDCHO protocol leveraged high order sliding modes to achieve exact consensus under a constrained set of initial conditions, limiting its applicability to static networks. In this work, we propose REDCHO, an extension of the previous protocol which is robust to mismatch in the initial conditions, making it suitable to use cases in which connection and disconnection of agents is possible. The convergence properties of the protocol are formally explored. Finally, the effectiveness and advantages of our proposal are shown with concrete simulation examples showing the benefits of REDCHO against other methods in the literature.

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arXiv2021

Differentiator for Noisy Sampled Signals with Best Worst-Case Accuracy

This paper proposes a differentiator for sampled signals with bounded noise and bounded second derivative. It is based on a linear program derived from the available sample information and requires no further tuning beyond the noise and derivative bounds. A tight bound on the worst-case accuracy, i.e., the worst-case differentiation error, is derived, which is the best among all causal differentiators and is moreover shown to be obtained after a fixed number of sampling steps. Comparisons with the accuracy of existing high-gain and sliding-mode differentiators illustrate the obtained results.

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arXiv2020

Autonomous Navigation of MAVs in Unknown Cluttered Environments

This paper presents an autonomous navigation framework for reaching a goal in unknown 3D cluttered environments. The framework consists of three main components. First, a computationally efficient method for mapping the environment from the disparity measurements obtained from a depth sensor. Second, a stochastic method to generate a path to a given goal, taking into account field of view constraints on the space that is assumed to be safe for navigation. Third, a fast method for the online generation of motion plans, taking into account the robot's dynamic constraints, model, and environmental uncertainty and disturbances. To highlight the contribution with respect to the available literature, we provide a qualitative and quantitative comparison with the state of the art methods for reaching a goal and for exploration in unknown environments, showing the superior performance of our approach. To illustrate the effectiveness of the proposed framework, we present experiments in multiple indoors and outdoors environments running the algorithm fully on board and in real-time, using a robotic platform based on the Intel Ready to Fly drone kit, which represents the implementation in the most frugal platform for navigation in unknown cluttered environments demonstrated to date. Open source code is available at:~\url{https://github.com/IntelLabs/autonomousmavs}. The video of the experimental results can be found at~\url{https://youtu.be/Wq0e7vF6nZM}.

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