A Generalized Time-Optimal Bi-Directional Scan Algorithm for Constrained Feedrate Optimization

2004 ◽  
Author(s):  
J. Dong ◽  
J. A. Stori
Keyword(s):  
Optimal Control ◽  
Optimization Algorithm ◽  
Optimal Solution ◽  
Computationally Efficient ◽  
Feedrate Optimization ◽  
State Dependent ◽  
Time Optimal ◽  
The Common ◽  
Computationally Intensive ◽  
Natural Way

The problem of generating an optimal feedrate trajectory has received a significant amount of attention in both the robotics and machining literature. The typical objective is to generate a minimum-time trajectory subject to constraints such as system limitations on actuator torques and accelerations. However, developing a computationally efficient solution to this problem while simultaneously guaranteeing optimality has proven challenging. The common constructive methods and optimal control approaches are computationally intensive. Heuristic methods have been proposed that reduce the computational burden but produce only near-optimal solutions with no guarantees. A two-pass feedrate optimization algorithm has been proposed previously in the literature by multiple researchers. However, no proof of optimality of the resulting solution has been provided. In this paper, the two-pass feedrate optimization algorithm is extended and generalized. The generalized algorithm maintains computationally efficiency, and supports the incorporation of a variety of state dependent constraints. By carefully arranging the local search steps, a globally optimal solution is achieved. Singularities, or critical points on the trajectory, which are difficult to deal with in optimal control approaches, are treated in a natural way in the generalized algorithm. A detailed proof is provided to show that the algorithm does generate a globally optimal solution under various types of constraints.

A Generalized Time-Optimal Bidirectional Scan Algorithm for Constrained Feed-Rate Optimization

2005 ◽  
Vol 128 (2) ◽  
pp. 379-390 ◽  
Author(s):  
J. Dong ◽  
J. A. Stori
Keyword(s):  
Optimal Control ◽  
Optimization Algorithm ◽  
Feed Rate ◽  
Optimal Solution ◽  
Global Optimality ◽  
Computationally Efficient ◽  
Time Optimal ◽  
Optimal Feed ◽  
Rate Optimization ◽  
Feed Rate Optimization

The problem of generating an optimal feed-rate trajectory has received a significant amount of attention in both the robotics and machining literature. The typical objective is to generate a minimum-time trajectory subject to constraints such as system limitations on actuator torques and accelerations. However, developing a computationally efficient solution to this problem while simultaneously guaranteeing optimality has proven challenging. The common constructive methods and optimal control approaches are computationally intensive. Heuristic methods have been proposed that reduce the computational burden but produce only near-optimal solutions with no guarantees. A two-pass feedrate optimization algorithm has been proposed previously in the literature by multiple researchers. However, no proof of optimality of the resulting solution has been provided. In this paper, the two-pass feed-rate optimization algorithm is generalized and a proof of global optimality is provided. The generalized algorithm maintains computational efficiency, and supports the incorporation of a variety of state-dependent constraints. By carefully arranging the local search steps, a globally optimal solution is achieved. Singularities, or critical points on the trajectory, which are difficult to deal with in optimal control approaches, are treated in a natural way in the generalized algorithm. A detailed proof is provided to show that the algorithm does generate a globally optimal solution under various types of constraints. Several examples are presented to illustrate the application of the algorithm.

scholarly journals Hidden invariant convexity for global and conic-intersection optimality guarantees in discrete-time optimal control

2021 ◽  
Author(s):  
Jorn H. Baayen ◽  
Krzysztof Postek
Keyword(s):  
Optimal Control ◽  
Power Systems ◽  
Discrete Time ◽  
Broad Class ◽  
Optimal Solution ◽  
Time Optimal Control ◽  
Exact Nature ◽  
State Variables ◽  
Numerical Experience ◽  
Time Optimal

AbstractNon-convex discrete-time optimal control problems in, e.g., water or power systems, typically involve a large number of variables related through nonlinear equality constraints. The ideal goal is to find a globally optimal solution, and numerical experience indicates that algorithms aiming for Karush–Kuhn–Tucker points often find solutions that are indistinguishable from global optima. In our paper, we provide a theoretical underpinning for this phenomenon, showing that on a broad class of problems the objective can be shown to be an invariant convex function (invex function) of the control decision variables when state variables are eliminated using implicit function theory. In this way, optimality guarantees can be obtained, the exact nature of which depends on the position of the solution within the feasible set. In a numerical example, we show how high-quality solutions are obtained with local search for a river control problem where invexity holds.

Determining Model Accuracy Requirements for Automotive Engine Coldstart Hydrocarbon Emissions Control

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Nasser L. Azad ◽  
Pannag R. Sanketi ◽  
J. Karl Hedrick
Keyword(s):  
Optimal Control ◽  
Sensitivity Analysis ◽  
Real Time ◽  
Minimum Principle ◽  
Optimal Solution ◽  
Control Performance ◽  
Automotive Engine ◽  
Engine Model ◽  
Time Optimal ◽  
Hc Emissions

In this work, a systematic method is introduced to determine the required accuracy of an automotive engine model used for real-time optimal control of coldstart hydrocarbon (HC) emissions. The engine model structure and development are briefly explained and the model predictions versus experimental results are presented. The control design problem is represented with a dynamic optimization formulation on the basis of the engine model and solved using the Pontryagin’s minimum principle (PMP). To relate the level of plant/model mismatch and the control performance degradation in practice, a sensitivity analysis using a computationally efficient method is employed. In this way, the sensitivities or the effects of small parameter variations on the optimal solution, which is the minimum of cumulative tailpipe HC emissions over the coldstart period, are calculated. There is a good agreement between the sensitivity analysis results and the experimental data. The sensitivities indicate the directions of the subsequent parameter estimation and model improvement tasks to enhance the control-relevant accuracy, and thus, the control performance. Furthermore, they provide some insights to simplify the engine model, which is critical for real-time implementation of the coldstart optimal control system.

scholarly journals An iterative method for time optimal control of dynamic systems

2011 ◽  
Vol 21 (1) ◽  
pp. 5-23 ◽  
Author(s):  
Navvab Kashiri ◽  
Mohammad Ghasemi ◽  
Morteza Dardel
Keyword(s):  
Optimal Control ◽  
Iterative Method ◽  
Dynamic Systems ◽  
Minimum Principle ◽  
Minimum Energy ◽  
Optimal Solution ◽  
Initial Guess ◽  
Open Loop ◽  
Time Optimal Control ◽  
Time Optimal

An iterative method for time optimal control of dynamic systemsAn iterative method for time optimal control of a general type of dynamic systems is proposed, subject to limited control inputs. This method uses the indirect solution of open-loop optimal control problem. The necessary conditions for optimality are derived from Pontryagin's minimum principle and the obtained equations lead to a nonlinear two point boundary value problem (TPBVP). Since there are many difficulties in finding the switching points and in solving the resulted TPBVP, a simple iterative method based on solving the minimum energy solution is proposed. The method does not need finding the switching point so that the resulted TPBVP can be solved by usual algorithms such as shooting and collocation. Also, since the solution of TPBVPs is sensitive to initial guess, a short procedure for making the proper initial guess is introduced. To this end, the accuracy and efficiency of the proposed method is demonstrated using time optimal solution of some systems: harmonic oscillator, robotic arm, double spring-mass problem with coulomb friction and F-8 aircraft.

Path constrained time-optimal motion of a cooperative two robot system

Robotica ◽  
1995 ◽  
Vol 13 (4) ◽  
pp. 363-374 ◽  
Author(s):  
Hye-Kyung Cho ◽  
Bum-Hee Lee ◽  
Myoung-Sam Ko
Keyword(s):  
Motion Planning ◽  
Optimal Solution ◽  
Problem Formulation ◽  
Planning Problem ◽  
Optimal Motion ◽  
Robot System ◽  
Admissible Region ◽  
Time Motion ◽  
State Dependent ◽  
Time Optimal

SummaryThis paper presents a systematic approach to the time-optimal motion planning of a cooperative two robot system along a prescribed path. First, the minimum-time motion planning problem is formulated in a concise form by parameterizing the dynamics of the robot system through a single variable describing the path. The constraints imposed on the input actuator torques and the exerted forces on the object are then converted into those on that variable, which result in the so-called admissible region in the phase plane of the variable. Considering the load distribution problem that is also involved in the motion, we present a systematic method to construct the admissible region by employing the orthogonal projection technique and the theory of multiple objective optimization. Especially, the effects of viscous damping and state-dependent actuator bounds are incorporated into the problem formulation so that the case where the admissible region is not simply connected can be investigated in detail. The resultant time-optimal solution specifies not only the velocity profile, but also the force assigned to each robot at each instant. Physical interpretation on the characteristics of the optimal actuator torques is also included with computer simulation results.

Vibration Reduction Using Near Time-Optimal Commands for Systems With Nonzero Initial Conditions

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Abhishek Dhanda ◽  
Joshua Vaughan ◽  
William Singhose
Keyword(s):  
Optimal Control ◽  
Initial Conditions ◽  
Vibration Reduction ◽  
Optimal Solution ◽  
Problem Formulation ◽  
Bridge Crane ◽  
Flexible Systems ◽  
Parametric Problem ◽  
Wide Range ◽  
Time Optimal

The control of flexible systems has been an active area of research for many years because of its importance to a wide range of applications. The majority of previous research on time-optimal control has concentrated on the rest-to-rest problem. However, there are many cases when flexible systems are not at rest or are subjected to disturbances. This paper presents an approach to design optimal vibration-reducing commands for systems with nonzero initial conditions. The problem is first formulated as an optimal control problem, and the optimal solution is shown to be bang-bang. Once the structure of the optimal command is known, a parametric problem formulation is presented for the computation of the switching times. Solutions are experimentally verified using a portable bridge crane by moving the payload through a commanded motion while removing initial payload swing.

Time-Optimal Control of Flexible Robots Made Robust Through Wave-Based Feedback

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
William J. O’Connor ◽  
David J. McKeown
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Robustness Analysis ◽  
Optimal Solution ◽  
Open Loop ◽  
Time Optimal Control ◽  
System Model ◽  
Optimal Control Strategy ◽  
Modeling Errors ◽  
Time Optimal

This paper presents a new, robust, time-optimal control strategy for flexible manipulators controlled by acceleration-limited actuators. The strategy is designed by combining the well-known, open-loop, time-optimal solution with wave-based feedback control. The time-optimal solution is used to design a new launch wave input to the wave-based controller, allowing it to recreate the time-optimal solution when the system model is exactly known. If modeling errors are present or a real actuator is used, the residual vibrations, which would otherwise arise when using the time-optimal solution alone, are quickly suppressed due to the additional robustness provided by the wave-based controller. A proximal time-optimal response is still achieved. A robustness analysis shows that significant improvements can be achieved using wave-based control in conjunction with the time-optimal solution. The implications and limits are also discussed.

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