Reducing Trajectory Tracking Error of Flexible Mobile Robots Using Command Shaping With Error-Limiting Constraints

2017 ◽  
Author(s):  
Gerald Eaglin ◽  
Joshua Vaughan
Keyword(s):  
Mobile Robots ◽  
Trajectory Tracking ◽  
Tracking Error ◽  
Input Shaping ◽  
Flexible Systems ◽  
Command Shaping ◽  
Modeling Errors ◽  
Temporal Tracking ◽  
Point Motion ◽  
Point To Point

The ability to track a trajectory without significant error is a vital requirement for mobile robots. Numerous methods have been proposed to mitigate tracking error. While these trajectory-tracking methods are efficient for rigid systems, many excite unwanted vibration when applied to flexible systems, leading to tracking error. This paper analyzes a modification of input shaping, which has been primarily used to limit residual vibration for point-to-point motion of flexible systems. Standard input shaping is modified using error-limiting constraints to reduce transient tracking error for the duration of the system’s motion. This method is simulated with trajectory inputs constructed using line segments and Catmull-Rom splines. Error-limiting commands are shown to improve both spatial and temporal tracking performance and can be made robust to modeling errors in natural frequency.

Friction-Compensating Command Shaping for Vibration Reduction

2004 ◽  
Vol 127 (4) ◽  
pp. 307-314 ◽  
Author(s):  
Jason Lawrence ◽  
William Singhose ◽  
Keith Hekman
Keyword(s):  
Steady State ◽  
Coulomb Friction ◽  
Vibration Reduction ◽  
Input Shaping ◽  
Residual Vibration ◽  
Command Shaping ◽  
Point Motion ◽  
Common Operation ◽  
Point To Point ◽  
Theoretical Developments

Fast and accurate point-to-point motion is a common operation for industrial machines, but vibration will frequently corrupt such motion. This paper develops commands that can move machines without vibration, even in the presence of Coulomb friction. Previous studies have shown that input shaping can be used on linear systems to produce point-to-point motion with no residual vibration. This paper extends command-shaping theory to nonlinear systems, specifically systems with Coulomb friction. This idea is applied to a PD-controlled mass with Coulomb friction to ground. The theoretical developments are experimentally verified on a solder cell machine. The results show that the new commands allow the proportional gain to be increased, resulting in reduced rise time, settling time, and steady-state error.

The Application of Command Shaping to the Tracking Problem

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Michael C. Reynolds ◽  
Peter H. Meckl
Keyword(s):  
Control Problem ◽  
Motion Control ◽  
Tracking Error ◽  
Tracking Problem ◽  
Command Shaping ◽  
Optimal Tracking ◽  
Tracking Technique ◽  
Optimal Input ◽  
Point Motion ◽  
Point To Point

This work presents a novel technique for the solution of an optimal input for trajectory tracking. Many researchers have documented the performance advantages of command shaping, which focuses on the design of an optimal input. Nearly all research in command shaping has been centered on the point-to-point motion control problem. However, tracking problems are also an important application of control theory. The proposed optimal tracking technique extends the point-to-point motion control problem to the solution of the tracking problem. Thus, two very different problems are brought into one solution scheme. The technique uses tolerances on trajectory following to meet constraints and minimize either maneuver time or input energy. A major advantage of the technique is that hard physical constraints such as acceleration or allowable tracking error can be directly constrained. Previous methods to perform such a task involved using various weightings that lack physical meaning. The optimal tracking technique allows for fast and efficient exploration of the solution space for motion control. A solution verification technique is presented and some examples are included to demonstrate the technique.

Experimental evaluation of time-varying impulse shaping with a two-link flexible manipulator

Robotica ◽  
1996 ◽  
Vol 14 (3) ◽  
pp. 339-345 ◽  
Author(s):  
Jung-Keun Cho ◽  
Youn-Sik Park
Keyword(s):  
Vibration Reduction ◽  
Vertical Plane ◽  
Joint Stiffness ◽  
Flexible Manipulator ◽  
Input Shaping ◽  
Time Varying ◽  
Modal Properties ◽  
Revolute Joints ◽  
Point Motion ◽  
Point To Point

SUMMARYIn the authors' previous paper,10 an input shaping method was presented to reduce motion-induced vibrations effectively for various classes of flexible systems. In this paper, the effectiveness of the shaping method is experimentally demonstrated with a two-link flexible manipulator systemThe manipulator for experiments includes two revolute joints and two flexible links, and moves on a vertical plane under gravity. An analytic model is developed considering the flexibility of the system and its joint stiffness in order to derive an appropriate estimation of dynamic modal properties. The input shaping method used in this work utilizes time-varying modal properties obtained from the model instead of the conventional input shaping method which employs time-invariant modal properties. A point-to-point motion is tested in order to show the effectivess of the proposed shaping method in vibration reduction during and after a given motion. The given reference trajectories are shaped to suppress the motion induced vibration. The test results demonstrate that the link vibration can be greatly suppressed during and after a motion, and the residual vibration reduction was observed more than 90% by employing this time-varying impulse shaping technique.

Joint input shaping and feedforward for point-to-point motion: Automated tuning for an industrial nanopositioning system

Mechatronics ◽  
2014 ◽  
Vol 24 (6) ◽  
pp. 572-581 ◽  
Author(s):  
Frank Boeren ◽  
Dennis Bruijnen ◽  
Niels van Dijk ◽  
Tom Oomen
Keyword(s):  
Input Shaping ◽  
Point Motion ◽  
Point To Point ◽  
Automated Tuning

Command Shaping Slewing Motions for Tower Cranes

2010 ◽  
Vol 132 (1) ◽  
Author(s):  
Jason Lawrence ◽  
William Singhose
Keyword(s):  
Nonlinear Dynamics ◽  
Rotational Motion ◽  
Effective Control ◽  
Input Shaping ◽  
Residual Vibration ◽  
Command Shaping ◽  
Tower Crane ◽  
Control Scheme ◽  
Point To Point ◽  
Gantry Cranes

Input shaping has been shown to be a practical and effective control scheme for reducing payload swing on industrial bridge and gantry cranes. However, when applied to tower cranes, standard input shapers will have degraded performance due to the nonlinear dynamics of rotational motion. To alleviate this problem, two new command generators for tower cranes are developed for a point-to-point slewing motion. It is shown that standard shaping techniques greatly reduce oscillation and the new tower crane command generators cause even less residual vibration. Simulations and experiments verify the results.

Fuzzy logic–based decision support system for selection of optimum input shaping techniques in point-to-point motion systems

2020 ◽  
pp. 095965182096570
Author(s):  
Hasan Huseyin Bilgic ◽  
Caglar Conker ◽  
Hakan Yavuz
Keyword(s):  
Fuzzy Logic ◽  
Decision Support ◽  
Decision Support System ◽  
Support System ◽  
Input Shaping ◽  
Advantages And Disadvantages ◽  
Shaping Technique ◽  
Point Motion ◽  
Point To Point ◽  
Selection Of

In this study, a novel fuzzy logic–based decision support system approach to provide assistance in the selection of suitable input shaping techniques is presented. The proposed approach selects the suitable input shaping technique for point-to-point motion type of systems such as precise positioning, crane operations, flexible robotic systems and so on. The problem solution addressed is the selection of the input shaping technique and the settings for the selection of the input shaper. Some of these design issues require extensive expertise in command shaping and system modeling studies. To overcome these problems and the necessity for such an expertise in these application areas, the proposed technique is provided as a solution. The presented study also provides a review of input shaping methods as well as their advantages and disadvantages in terms of vibration elimination performance, traveling time and robustness features. In the final section of the study, the details of the simulations, as well as experimental results, are provided to validate the achieved high performance of the proposed technique. The experimental studies are conducted on a Quanser IP02 Gantry Crane experimental setup.

New Command Shaping Methods for Reduced Vibration of a Suspended Payload With Constrained Trolley Motion

2007 ◽  
Author(s):  
Aaron R. Enes ◽  
Timothy Y. Hsu ◽  
Angela A. Sodemann
Keyword(s):  
System Modeling ◽  
Small Scale ◽  
Residual Vibration ◽  
Conveyor System ◽  
Command Shaping ◽  
Common Task ◽  
Modeling Errors ◽  
Point To Point ◽  
Manufacturing Environments ◽  
Command Signal

In manufacturing environments, a common task is to quickly move a suspended payload point-to-point along a fixed overhead conveyor track without inducing significant payload vibration. Recent research in command shaping has shown remarkably effective ways to reduce the swing of a suspended payload providing the motion of the trolley is not constrained. However, the development of a command shaper where the trajectory of the trolley is constrained to follow a fixed curvilinear path has not been explored. This paper will present the development of a simple feedforward command shaper for fast, low vibration, point-to-point movement of a payload suspended from a trolley constrained to follow a fixed generalized path. The command shaping method involves modifying the command signal by convolving it with a series of impulses. Prior work has suggested command shaping to be very effective for fast, low-vibration movement of flexible systems. In this paper, command shaping methods are applied to an overhead conveyor system constrained to move along a fixed curvilinear path. Two new command shapers are presented for canceling payload vibration induced by motion of the trolley along the path. The designed Tangential Vibration (TV) shaper reduces payload vibrations induced by tangential accelerations of the trolley along the path, while the Centripetal-Tangential Vibration (CTV) shaper reduces vibrations induced by both tangential and centripetal accelerations. A key result of this study is that a command shaper having at least three impulses is required to yield zero residual vibration for motion along a curvilinear path. A simple pendulum payload attached to an actual small-scale overhead trolley following a constrained path is used to evaluate the performance of the designed command shapers. It is shown that the designed shapers significantly reduce payload swing compared to unshaped performance. An experimental sensitivity analysis shows the designed shapers are robust to system modeling errors and variations in path parameters.

An Alternative for Trajectory Tracking in Mobile Robots Applying Differential Flatness

2013 ◽  
pp. 148-160
Author(s):  
Elkin Yesid Veslin Díaz ◽  
Jules G. Slama ◽  
Max Suell Dutra ◽  
Omar Lengerke Pérez ◽  
Hernán Gonzalez Acuña
Keyword(s):  
Mobile Robot ◽  
Mobile Robots ◽  
Trajectory Tracking ◽  
Differential Flatness ◽  
Boundary Values ◽  
Route Finding ◽  
Point To Point

One solution for trajectory tracking in a non-holonomic vehicle, like a mobile robot, is proposed in this chapter. Using the boundary values, a desired route is converted into a polynomial using a point-to-point algorithm. With the properties of Differential Flatness, the system is driven along this route, finding the necessary input values so that the system can perform the desired movement.

Command Shaping for Flexible Systems Subject to Constant Acceleration Limits

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Jon Danielson ◽  
Jason Lawrence ◽  
William Singhose
Keyword(s):  
Effective Means ◽  
Input Shaping ◽  
Constant Force ◽  
Flexible Systems ◽  
Common Occurrence ◽  
Constant Acceleration ◽  
Command Shaping ◽  
Input Shaper ◽  
Drive Systems ◽  
Theoretical Results

Input shaping is an effective means of eliminating vibration in many types of flexible systems. This paper discusses how input shaper performance is affected by a fixed acceleration limit. This type of limit is a common occurrence in many mechanical drive systems because it corresponds to a constant force or torque input. It is shown that some input shapers are not affected by an acceleration limit under certain conditions. A test criterion is developed to determine what types of input shapers are negatively affected, and a method is proposed to compensate for the detrimental effects of the constant acceleration limit. Experimental results from an industrial crane support the main theoretical results.

Linear algebra-based controller for trajectory tracking in mobile robots with additive uncertainties estimation

2019 ◽  
Vol 37 (2) ◽  
pp. 607-624
Author(s):  
G J E Scaglia ◽  
M E Serrano ◽  
S A Godoy ◽  
F Rossomando
Keyword(s):  
Mobile Robots ◽  
Linear Algebra ◽  
Trajectory Tracking ◽  
Controller Design ◽  
Design Method ◽  
Tracking Error ◽  
Experimental Tests ◽  
Monte Carlo Experiment ◽  
Algebra Theory ◽  
Proof Of Convergence

Abstract This paper addresses trajectory tracking problem in mobile robots considering additive uncertainties. The controller design method is based on linear algebra theory. Numerical estimation techniques are used to estimate the uncertainty value in each sample time. The controller is calibrated by stochastic way using the Monte Carlo Experiment. In addition, the proof of convergence to zero of the tracking error is included. The theoretical results are validated by simulation and experimental tests. The controller proposed shows that it can be used to reduce the effect of additive uncertainties in the tracking error.

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