arXiv subjects

David Gómez-Gutiérrez

Publications and source records attributed to David Gómez-Gutiérrez.

14 recordsLinked to original sources

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.

eess.SY↗

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.

math.OC↗

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.

math.OC↗

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.

math.OC↗

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.

eess.SY↗

arXiv2021

On finite-time and fixed-time consensus algorithms for dynamic networks switching among disconnected digraphs

The aim of this paper is to analyze a class of consensus algorithms with finite-time or fixed-time convergence for dynamic networks formed by agents with first-order dynamics. In particular, in the analyzed class a single evaluation of a nonlinear function of the consensus error is performed per each node. The classical assumption of switching among connected graphs is dropped here, allowing to represent failures and intermittent communications between agents. Thus, conditions to guarantee finite and fixed-time convergence, even while switching among disconnected graphs, are provided. Moreover, the algorithms of the considered class are shown to be computationally simpler than previously proposed finite-time consensus algorithms for dynamic networks, which is an important feature in scenarios with computationally limited nodes and energy efficiency requirements such as in sensor networks. The performance of the considered consensus algorithms is illustrated through simulations, comparing it to existing approaches for dynamic networks with finite-time and fixed-time convergence. It is shown that the settling time of the considered algorithms grows slower when the number of nodes increases than with other consensus algorithms for dynamic networks.

eess.SY↗

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.

math.OC↗

arXiv2020

Predefined-Time Consensus of High-Order Multi-Agent Systems

This paper addresses the distributed prescribed-time leader-following consensus problem for a class of high-order multi-agent systems (MASs) with perturbed nonlinear agents dynamics and where the topology of the network contains a directed spanning tree, with the leader as the root. Prescribed-time consensus means that an agreement state of the MAS is achieved in a preset time, introduced as a parameter of the control law, and this constant settling time is achieved independently of the agents' initial state. The proposed control method exhibits three main advantages: first, to our best knowledge, it is the first time that prescribed-time convergence in a consensus problem is achieved for agents with high-order nonlinear dynamics, using a robust leader-following protocol, which allows an effective rejection of matched disturbances in the agents' model. Second, the proposed controller provides control signals of lower magnitude than existing approaches. Third, the proposed consensus protocol does not have parameters to be adjusted depending on the connectivity of the considered communication graph.

eess.SY↗

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}.

cs.RO↗

arXiv2020

On the design of non-autonomous fixed-time controllers with a predefined upper bound of the settling time

This paper aims to introduce a design methodology to stabilize a chain of integrators in a fixed-time with predefined Upper Bound for the Settling-Time (UBST). This approach is based on time-varying gains (time-base generator) that become singular as the time approaches the predefined convergence time. We present the conditions such that every nonzero trajectory convergence exactly at the predefined time with feedback laws that are simpler than in previous approaches. Additionally, we present results such that the origin is reached before the singularity occurs, making this approach realizable in practice. A significant contribution, since current results, based on time-varying gains, required the time-varying gain to tend to infinity as the time approaches the prescribed/predefined-time. Moreover, our approach guarantees fixed-time convergence with predefined UBST even in the presence of bounded disturbances (with known bound) and provides a methodology to re-design an autonomous fixed-time controller where the estimate of the UBST for the closed-loop system is very conservative into a less conservative one with predefined \textit{UBST} that can be set arbitrarily tight. We present numerical examples to illustrate the effectiveness of the approach together with comparisons with existing autonomous fixed-time controllers.

math.OC↗

arXiv2020

Consistent Discretization of a Class of Predefined-Time Stable Systems

As the main contribution, this document provides a consistent discretization of a class of fixed-time stable systems, namely predefined-time stable systems. In the unperturbed case, the proposed approach allows obtaining not only a consistent but exact discretization of the considered class of predefined-time stable systems, whereas in the perturbed case, the consistent discretization preserves the predefined-time stability property. All the results are validated through simulations and compared with the conventional explicit Euler scheme, highlighting the advantages of this proposal.

math.OC↗

arXiv2020

A methodology for designing fixed-time stable systems with a predefined upper-bound in their settling time

Algorithms having uniform convergence with respect to their initial condition (i.e., with fixed-time stability) are receiving increasing attention for solving control and observer design problems under time constraints. However, we still lack a general methodology to design these algorithms for high-order perturbed systems when we additionally need to impose a user-defined upper-bound on their settling time, especially for systems with perturbations. Here, we fill this gap by introducing a methodology to redesign a class of asymptotically, finite- and fixed-time stable systems into non-autonomous fixed-time stable systems with a user-defined upper-bound on their settling time. Our methodology redesigns a system by adding time-varying gains. However, contrary to existing methods where the time-varying gains tend to infinity as the origin is reached, we provide sufficient conditions to maintain bounded gains. We illustrate our methodology by building fixed-time online differentiators with user-defined upper-bound on their settling time and bounded gains.

math.OC↗

arXiv2019

A Hybrid Method for Online Trajectory Planning of Mobile Robots in Cluttered Environments

This paper presents a method for online trajectory planning in known environments. The proposed algorithm is a fusion of sampling-based techniques and model-based optimization via quadratic programming. The former is used to efficiently generate an obstacle-free path while the latter takes into account the robot dynamical constraints to generate a time-dependent trajectory. The main contribution of this work lies on the formulation of a convex optimization problem over the generated obstacle-free path that is guaranteed to be feasible. Thus, in contrast with previously proposed methods, iterative formulations are not required. The proposed method has been compared with state-of-the-art approaches showing a significant improvement in success rate and computation time. To illustrate the effectiveness of this approach for online planning, the proposed method was applied to the fluid autonomous navigation of a quadcopter in multiple environments consisting of up to two hundred obstacles. The scenarios hereinafter presented are some of the most densely cluttered experiments for online planning and navigation reported to date. See video at https://youtu.be/DJ1IZRL5t1Q

cs.RO↗

arXiv2019

Real-time Approximate Bayesian Computation for Scene Understanding

Consider scene understanding problems such as predicting where a person is probably reaching, or inferring the pose of 3D objects from depth images, or inferring the probable street crossings of pedestrians at a busy intersection. This paper shows how to solve these problems using Approximate Bayesian Computation. The underlying generative models are built from realistic simulation software, wrapped in a Bayesian error model for the gap between simulation outputs and real data. The simulators are drawn from off-the-shelf computer graphics, video game, and traffic simulation code. The paper introduces two techniques for speeding up inference that can be used separately or in combination. The first is to train neural surrogates of the simulators, using a simple form of domain randomization to make the surrogates more robust to the gap between the simulation and reality. The second is to adaptively discretize the latent variables using a Tree-pyramid approach adapted from computer graphics. This paper also shows performance and accuracy measurements on real-world problems, establishing that it is feasible to solve these problems in real-time.

cs.CV↗