Time Optimal Trajectories for a Mobile Robot Under Nonsliding and Radius-of-Turn Constraints

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Joseph Z. Ben-Asher ◽  
Michael Wetzler ◽  
Elon D. Rimon
Keyword(s):  
Optimal Control ◽  
Mobile Robot ◽  
Numerical Solutions ◽  
Optimal Path ◽  
Linear Acceleration ◽  
Optimal Trajectories ◽  
Hodograph Method ◽  
Minimal Radius ◽  
Time Optimal ◽  
Target States

Abstract The time-optimal path problem for a point mass mobile robot is considered. Given initial and target states, we seek the time optimal path subject to the following constraints: (1) A limitation on its maximal linear acceleration; (2) a speed-dependent nonsliding condition; and (3) a minimal radius of turn. The paper formulates and analyzes the time optimal path problem using standard optimal control formulation with extensive use of the classical Hodograph method. Based on the analysis, the time optimal path consists of five path primitives. Numerical solutions are obtained to support and illustrate the analysis.

Time Optimal Trajectories for a Mobile Robot With Acceleration and Speed Limits in the Presence of an Obstacle

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
J. Z. Ben-Asher ◽  
E. D. Rimon ◽  
M. Wetzler ◽  
J. Diepolder
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Mobile Robot ◽  
Control Problem ◽  
Point Mass ◽  
Optimal Trajectories ◽  
Speed Limits ◽  
Optimal Paths ◽  
Time Optimal ◽  
Turn Rate

Abstract This paper studies the time optimal paths of a mobile robot navigating in a planar environment containing an obstacle. The paper considers a point-mass robot that moves with bounded acceleration and limited turn-rate controls in the presence of an obstacle. The optimal control problem yields 12 path primitives that form the time optimal paths of the point-mass robot. The problem is then extended to a disc-robot that moves in the presence of an obstacle with turn in-place capability. The optimality conditions yield 12 modified path primitives that form the time optimal paths of the disc-robot. All path primitives are analytically characterized and examples demonstrate how they form time optimal trajectories in the presence of several obstacle types.

scholarly journals A Numerical Computation Approach for the Optimal Control of ASP Flooding Based on Adaptive Strategies

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Shurong Li ◽  
Yulei Ge
Keyword(s):  
Optimal Control ◽  
Numerical Computation ◽  
Numerical Solutions ◽  
Pseudospectral Method ◽  
Adaptive Strategies ◽  
Terminal Condition ◽  
Constraint Aggregation ◽  
Asp Flooding ◽  
Time Optimal ◽  
Ks Function

A numerical computation approach based on constraint aggregation and pseudospectral method is proposed to solve the optimal control of alkali/surfactant/polymer (ASP) flooding. At first, all path constraints are aggregated into one terminal condition by applying a Kreisselmeier-Steinhauser (KS) function. After being transformed into a multistage problem by control vector parameter, a normalized time variable is introduced to convert the original problem into a fixed final time optimal control problem. Then the problem is discretized to nonlinear programming by using Legendre-Gauss pseudospectral method, whose numerical solutions can be obtained by sequential quadratic programming (SQP) method through solving the KKT optimality conditions. Additionally, two adaptive strategies are applied to improve the procedure: (1) the adaptive constraint aggregation is used to regulate the parameter ρ in KS function and (2) the adaptive Legendre-Gauss (LG) method is used to adjust the number of subinterval divisions and LG points. Finally, the optimal control of ASP flooding is solved by the proposed method. Simulation results show the feasibility and effectiveness of the proposed method.

scholarly journals On the construction of nearly time optimal continuous feedback laws around switching manifolds

2020 ◽  
Vol 26 ◽  
pp. 4
Author(s):  
Fabio Ancona ◽  
Cristopher Hermosilla
Keyword(s):  
Optimal Control ◽  
Initial Data ◽  
Optimal Trajectories ◽  
Optimal Feedback ◽  
External Perturbations ◽  
Starting Point ◽  
Time Optimal ◽  
Continuous Feedback ◽  
Time Optimal Control Problem ◽  
Feedback Laws

In this paper, we address the question of the construction of a nearly time optimal feedback law for a minimum time optimal control problem, which is robust with respect to internal and external perturbations. For this purpose we take as starting point an optimal synthesis, which is a suitable collection of optimal trajectories. The construction we exhibit depends exclusively on the initial data obtained from the optimal feedback which is assumed to be known.

Novel three-dimensional optimal path planning method for vehicles with constrained pitch and yaw

Robotica ◽  
2016 ◽  
Vol 35 (11) ◽  
pp. 2157-2176 ◽  
Author(s):  
B. Wehbe ◽  
S. Bazzi ◽  
E. Shammas
Keyword(s):  
Path Planning ◽  
Optimal Path ◽  
Three Dimensional ◽  
Vertical Motion ◽  
The Body ◽  
Planning Method ◽  
Optimal Trajectories ◽  
Planning Problem ◽  
Body Frame ◽  
Time Optimal

SUMMARYThis paper presents a novel method for generating three-dimensional optimal trajectories for a vehicle or body that moves forward at a constant speed and steers in both horizontal and vertical directions. The vehicle's dynamics limit the body-frame pitch and yaw rates; additionally, the climb and decent angles of the vehicle are also bounded. Given the above constraints, the path planning problem is solved geometrically by building upon the two-dimensional Dubins curves and then Pontryagin's Maximum Principle is used to validate that the proposed solution lies within the family of candidate time-optimal trajectories. Finally, given the severe boundedness constraints on the vertical motion of the system, the robustness of the proposed path planning method is validated by naturally extending it to remain applicable to high-altitude final configurations.

TIME-OPTIMAL PATH PLANNING AND CONTROL USING NEURAL NETWORKS AND A GENETIC ALGORITHM

2002 ◽  
Vol 02 (02) ◽  
pp. 153-172 ◽  
Author(s):  
NACHOL CHAIYARATANA ◽  
ALI M. S. ZALZALA
Keyword(s):  
Genetic Algorithm ◽  
Neural Networks ◽  
Optimal Control ◽  
Position Control ◽  
Optimal Path ◽  
Tracking Error ◽  
Time Optimal Control ◽  
Coding Schemes ◽  
Time Optimal ◽  
Kohonen Networks

This paper presents the use of neural networks and a genetic algorithm in time-optimal control of a closed-loop 3-dof robotic system. Extended Kohonen networks which contain an additional lattice of output neurons are used in conjunction with PID controllers in position control to minimize command tracking errors. The extended Kohonen networks are trained using reinforcement learning where the overall learning algorithm is derived from a self-organizing feature-mapping algorithm and a delta learning rule. The results indicate that the extended Kohonen network controller is more efficient than other techniques reported in early literature when the robot is operated under normal conditions. Subsequently, a multi-objective genetic algorithm (MOGA) is used to solve an optimization problem related to time-optimal control. This problem involves the selection of actuator torque limits and an end-effector path subject to time-optimality and tracking error constraints. Two chromosome coding schemes are explored in the investigation: Gray and integer-based coding schemes. The results suggest that the integer-based chromosome is more suitable at representing the decision variables. As a result of using both neural networks and a genetic algorithm in this application, an idea of a hybridization between a neural network and a genetic algorithm at the task level for use in a control system is also effectively demonstrated.

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