Optimal trajectories for nonholonomic mobile robots

Souères, Philippe; Boissonnat, Jean‐Daniel

doi:10.1007/bfb0036072

Cited by 86 publications

(77 citation statements)

References 18 publications

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“…Note that the feedback gain K * P (t), t ∈ I , is now used to find the optimal input error signalũ(t) using (8). The actual optimal control input can then be found simply by u * (t) = u d (t) +ũ(t).…”

Section: T)mentioning

confidence: 99%

“…This section illustrates the robustness of the feedback control law (8). The robustness result for model (1) presented in this section is an immediate consequence of controlling semi-linear dynamic systems with limited uncertainty illustrated in [33].…”

Section: Robustnessmentioning

confidence: 99%

“…We now form the robot's feedback system as in (9) using the feedback control (8). Hence, the optimal time-varying feedback gain K * P (t) ∈ K ad ⊂ R 2×3 , for t ∈ I ≡ [0, 60] s, will drive the system (36) such that e(t) → 0, andũ(t) → 0, for t ∈ I .…”

Section: Example 1: Wheeled Mobile Robotmentioning

confidence: 99%

“…Several control laws have been proposed in [6][7][8][9], which are based on basic optimal control theory. A large body of research work has been conducted on Model Predictive Control (MPC) schemes that rely on the solution of an open-loop optimal control problem to predict the system behavior over a time horizon [10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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Optimal time-varying P-controller for a class of uncertain nonlinear systems

Miah

Gueaieb

2014

Int. J. Control Autom. Syst.

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In this manuscript, an optimal time-varying P-controller is presented for a class of continuous-time underactuated nonlinear systems in the presence of process noise associated with systems' inputs. This is a state feedback control strategy where the optimization is performed on a time-varying feedback operator (herein called the feedback control gain). The main goal of the current manuscript is to provide a framework for multi-input multi-output nonlinear systems which yields a satisfactory tracking performance based on the optimal time-varying feedback control gain. Unlike other feedback control techniques that perform dynamic linearization of system models, the proposed time-varying P-controller provides the full-state feedback control to the original nonlinear system model. Hence, this P-controller guarantees global asymptotic statetracking. Furthermore, the bounded system's process noise is taken into consideration to measure the controller's robustness. The proposed P-controller is tested for its nonlinear trajectory tracking and fixed-point stabilization capabilities with two nonholonomic systems in the presence of actuators' noise.

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Section: T)mentioning

confidence: 99%

Section: Robustnessmentioning

confidence: 99%

Section: Example 1: Wheeled Mobile Robotmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal time-varying P-controller for a class of uncertain nonlinear systems

Miah

Gueaieb

2014

Int. J. Control Autom. Syst.

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“…Boissonnat et al [6] propose a dynamic extension of Dubins car problem by constraining the angular acceleration of the agent instead of its angular velocity. Some researchers consider problems with a more complex mobile robot configuration such as trailer-truck systems navigation [65]. Chitsaz and LaValle [13], on the other hand, extend Dubins car to having altitude, leading to problems studying a time-optimal trajectory for airplanes.…”

Section: Related Workmentioning

confidence: 99%

Optimal path finding in direction, location, and time dependent environments

Dolinskaya

2012

Naval Research Logistics

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This article examines optimal path finding problems where cost function and constraints are direction, location, and time dependent. Recent advancements in sensor and data‐processing technology facilitate the collection of detailed real‐time information about the environment surrounding a ground vehicle, an airplane, or a naval vessel. We present a navigation model that makes use of such information. We relax a number of assumptions from existing literature on path‐finding problems and create an accurate, yet tractable, model suitable for implementation for a large class of problems. We present a dynamic programming model which integrates our earlier results for direction‐dependent, time and space homogeneous environment, and consequently, improves its accuracy, efficiency, and run‐time. The proposed path finding model also addresses limited information about the surrounding environment, control‐feasibility of the considered paths, such as sharpest feasible turns a vehicle can make, and computational demands of a time‐dependent environment. To demonstrate the applicability and performance of our path‐finding algorithm, computational experiments for a short‐range ship routing in dynamic wave‐field problem are presented. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

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Time-Optimal Motion of Spatial Dubins Systems

Wang

Balkcom

2020

Springer Proceedings in Advanced Robotics

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Optimal trajectories for nonholonomic mobile robots

Cited by 86 publications

References 18 publications

Optimal time-varying P-controller for a class of uncertain nonlinear systems

Optimal time-varying P-controller for a class of uncertain nonlinear systems

Optimal path finding in direction, location, and time dependent environments

Time-Optimal Motion of Spatial Dubins Systems

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