Adaptive Backstepping of Synergistic Hybrid Feedbacks with Application to Obstacle Avoidance
10 Jul 2019-pp 1730-1735
TL;DR: The hybrid controller induced by a Synergistic Lyapunov Function and Feedback pair relative to a compact set can be extended to the case where the original affine control system is subject to a class of additive disturbances known as matched uncertainties, provided that the estimator dynamics do not add new equilibria to the closed-loop system.
Abstract: In this paper, we show that the hybrid controller that is induced by a Synergistic Lyapunov Function and Feedback (SLFF) pair relative to a compact set, can be extended to the case where the original affine control system is subject to a class of additive disturbances known as matched uncertainties, provided that the estimator dynamics do not add new equilibria to the closed-loop system. We also show that the proposed adaptive hybrid controller is amenable to backstepping. Finally, we apply the proposed hybrid control strategy to the problem of global asymptotic stabilization of a compact set in the presence of an obstacle and we illustrate this application by means of simulation results.
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01 Jun 1996
103 citations
25 May 2021
TL;DR: In this article, a synergistic CBF for obstacle avoidance for nonholonomic vehicles is constructed by shifting the orientations with vanishing control authority, where a logic variable is used to determine the preferred direction.
Abstract: Control barrier functions (CBFs) have recently emerged as a means to ensure safety of controlled dynamical systems. CBFs are suitable for obstacle avoidance, where the CBF is often constructed from the distance and relative velocity between the vehicle and the obstacle. For vehicles required to maintain non-zero forward speed, ordinary (non-hybrid) CBFs cannot ensure safety due to vanishing control authority when the vehicle is oriented directly towards the obstacle. In this paper, synergistic CBFs are proposed, which is an intuitive extension of CBFs using ideas from synergistic Lyapunov functions. A synergistic CBF for obstacle avoidance for nonholonomic vehicles is constructed by shifting the orientations with vanishing control authority. This induces a penalty for traversing the obstacle in the counterclockwise or clockwise direction, where a logic variable is used to determine the preferred direction. The performance of the CBF is illustrated by a case study.
13 citations
TL;DR: In this paper , the authors developed a composite guiding vector field via the use of smooth bump functions and provided theoretical guarantees that the integral curves of the vector field can follow an arbitrary sufficiently smooth desired path and avoid collision with obstacles of arbitrary shapes.
Abstract: Accurately following a geometric desired path in a two-dimensional (2-D) space is a fundamental task for many engineering systems, in particular mobile robots. When the desired path is occluded by obstacles, it is necessary and crucial to temporarily deviate from the path for obstacle/collision avoidance. In this article, we develop a composite guiding vector field via the use of smooth bump functions and provide theoretical guarantees that the integral curves of the vector field can follow an arbitrary sufficiently smooth desired path and avoid collision with obstacles of arbitrary shapes. These two behaviors are reactive since path (re)planning and global map construction are not involved. To deal with the common deadlock problem, we introduce a switching vector field, and the Zeno behavior is excluded. Simulations are conducted to support the theoretical results.
6 citations
TL;DR: In this article , an adaptive hybrid feedback control law for global asymptotic tracking of a hybrid reference system for marine vehicles in the presence of parametric modeling errors is presented.
Abstract: This article presents an adaptive hybrid feedback control law for global asymptotic tracking of a hybrid reference system for marine vehicles in the presence of parametric modeling errors. The reference system is constructed from a parameterized loop and a speed assignment specifying the motion along the path, which decouples the geometry of the path from the motion along the path. During flows, the hybrid feedback consists of a proportional-derivative action and an adaptive feedforward term, while a hysteretic switching mechanism that is independent of the vehicle velocities determines jumps. The effectiveness of the proposed control law is demonstrated through experiments.
2 citations
06 Dec 2022
TL;DR: In this article , a generalized definition of synergistic Lyapunov functions and feedbacks is proposed, which allows the logic variable in traditional synergistic control, denoted the synergy variable, to be vector-valued and change during flows.
Abstract: This paper generalizes results on synergistic hybrid feedback control. Specifically, we propose a generalized definition of synergistic Lyapunov functions and feedbacks which allows the logic variable in traditional synergistic control, denoted the synergy variable, to be vector-valued and change during flows. Moreover, we introduce synergy gaps relative to components of product sets, which enables us to define jump conditions in the form of synergy gaps for different components of the synergy variable. In particular, this enables us to formulate existing hybrid output feedback control schemes within the synergistic control framework. Furthermore, we show that our generalized definition is amenable to backstepping. Finally, we give an example of how traditional synergistic control can be combined with ship maneuvering control with discrete path dynamics.
2 citations
References
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Book•
18 Mar 2012
TL;DR: This book presents a complete theory of robust asymptotic stability for hybrid dynamical systems that is applicable to the design of hybrid control algorithms--algorithms that feature logic, timers, or combinations of digital and analog components.
Abstract: Hybrid dynamical systems exhibit continuous and instantaneous changes, having features of continuous-time and discrete-time dynamical systems. Filled with a wealth of examples to illustrate concepts, this book presents a complete theory of robust asymptotic stability for hybrid dynamical systems that is applicable to the design of hybrid control algorithms--algorithms that feature logic, timers, or combinations of digital and analog components. With the tools of modern mathematical analysis, Hybrid Dynamical Systems unifies and generalizes earlier developments in continuous-time and discrete-time nonlinear systems. It presents hybrid system versions of the necessary and sufficient Lyapunov conditions for asymptotic stability, invariance principles, and approximation techniques, and examines the robustness of asymptotic stability, motivated by the goal of designing robust hybrid control algorithms. This self-contained and classroom-tested book requires standard background in mathematical analysis and differential equations or nonlinear systems. It will interest graduate students in engineering as well as students and researchers in control, computer science, and mathematics.
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"Adaptive Backstepping of Synergisti..." refers background in this paper
...The definitions of global uniform pre-asymptotic stability and invariance can be found in [1]....
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TL;DR: In this article, it was shown that a continuous dynamical system on a state space that has the structure of a vector bundle on a compact manifold possesses no globally asymptotically stable equilibrium.
790 citations
TL;DR: In this paper, a class of scalar valued analytic maps on analytic manifolds with boundary is constructed on an arbitrary sphere world, a compact connected subset of Euclidean n-space whose boundary is formed from the disjoint union of a finite number of (n - l)-spheres.
577 citations
"Adaptive Backstepping of Synergisti..." refers background in this paper
...However, it was shown in [13] that in a spherical state space, there is at least one saddle equilibrium point for each obstacle within the state space, thus precluding global asymptotic stabilization of a setpoint by continuous feedback....
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Book•
13 Jun 1996TL;DR: In this paper, the authors introduce students to optimization theory and its use in economics and allied disciplines, and provide a number of detailed examples explaining both the theory and their applications for first-year master's and graduate students.
Abstract: This book, first published in 1996, introduces students to optimization theory and its use in economics and allied disciplines. The first of its three parts examines the existence of solutions to optimization problems in Rn, and how these solutions may be identified. The second part explores how solutions to optimization problems change with changes in the underlying parameters, and the last part provides an extensive description of the fundamental principles of finite- and infinite-horizon dynamic programming. Each chapter contains a number of detailed examples explaining both the theory and its applications for first-year master's and graduate students. 'Cookbook' procedures are accompanied by a discussion of when such methods are guaranteed to be successful, and, equally importantly, when they could fail. Each result in the main body of the text is also accompanied by a complete proof. A preliminary chapter and three appendices are designed to keep the book mathematically self-contained.
509 citations
01 Jul 1990
TL;DR: Contents: Guidance (Kinematics, Control, and Trajectory Generation), Sensors, Navigation, Maps Representation, Sensing Strategies, Motion Planning, Systems.
Abstract: Contents: Guidance (Kinematics, Control, and Trajectory Generation.- Sensors.- Navigation (Position and Copurse Estimation).- Map Representation.- Sensing Strategies.- Motion Planning.- Systems.
503 citations