A Minimum-Jerk Speed-Planning Algorithm for Coordinated Planning and Control of Automated Assembly Manufacturing

Gyorfi, J.S.; Wu, Chia‐Ju

doi:10.1109/tase.2005.860987

Cited by 15 publications

(8 citation statements)

References 30 publications

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“…The literature for the second approach usually focuses on either the discrete optimization problem of covering a point set or the continuous optimization problem of trajectory generation [20], [14]. The problem of covering a point set by a single robot with collision avoidance constraints has been studied for industrial robots [24], [32], [28], [3].…”

Section: Related Literaturementioning

confidence: 99%

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Coverage of a Planar Point Set With Multiple Robots Subject to Geometric Constraints

Chakraborty

Akella

Wen

2010

IEEE Trans. Automat. Sci. Eng.

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This paper focuses on the assignment of discrete points among geometrically constrained robots and determination of the order in which the points should be processed by the robots. This path planning problem is directly motivated by an industrial laser drilling system with two robots that are constrained to translate along a common line while satisfying collision avoidance constraints. The points lie on a planar base plate that translates normal to the axis of motion of the robots. The geometric constraints on the motions of the robots lead to constraints on points that can be processed simultaneously.We use a two step approach to solve the path planning problem: 1) Splitting Problem: Assign the points to the robots, subject to geometric constraints, to maximize parallel processing of the points. 2) Ordering Problem: Find an order of processing the split points by formulating and solving a multidimensional Traveling Salesman Problem (TSP) in the -tuple space with an appropriately defined metric to minimize the total travel cost. For = 2, we solve the splitting problem optimally in ( 3 ) time by converting it to a maximum cardinality matching problem. Since this is too slow for large datasets, we also provide a greedy ( log ) algorithm. We provide computational results showing that the greedy algorithm solution is very close to the optimal solution for large datasets. For the ordering problem we present local search based heuristics to improve the multidimensional TSP tour. We give computational results for the ordering problem and for the overall performance gain obtained (over a single robot system) by using our algorithm. Finally, we extend our approach to a -robot system and give computational results for = 4.Note to Practitioners-This paper presents techniques to plan the motions of multiple robots to visit and process a given set of points, subject to geometric constraints on the robot motions. This point set coverage task is motivated by a laser drilling application for electronics manufacturing. The goal is to minimize the time taken to visit the points by parallelizing the robot operations while avoiding robot collisions. Similar tasks arise in many applications including drilling, electronics manufacturing, circuit testing, spot welding, and sensor network data collection. We model the assign-

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Section: Related Literaturementioning

confidence: 99%

“…Equation (12) states that each point should be visited only once and (13) implies that a robot can only be at one particular point at a time. Equation (14) states that the total number of points that have to covered by all the robots is whereas (15) implies that at a given time , at most points can be processed.…”

Section: Appendixmentioning

confidence: 99%

Coverage of a Planar Point Set With Multiple Robots Subject to Geometric Constraints

Chakraborty

Akella

Wen

2010

IEEE Trans. Automat. Sci. Eng.

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“…Gasparetto and colleagues 15,26 introduced a minimum time-jerk trajectory planning algorithm of which objective function was to reach a reasonable compromise between the overall task execution time and the total integral value of squared jerk. For the sake of formulation of minimum-jerk trajectory planning for surface-mount assembly robots, Gyorfi and Wu 25 utilized the discretized quintic polynomial curve to obtain an expected trajectory with appealing smoothness and jerk-limited property. To cope with a notable constrained velocity-level path planning issue for traditional mobile robots, Guarino Lo Bianco 32 introduced a seven-segment parabolic velocity curve to fulfill the complicated minimum-jerk trajectory planning assignment of which objective was to minimize the maximum of longitudinal jerk.…”

Section: Introductionmentioning

confidence: 99%

“…the third-order derivative of position curve with time). [23][24][25][26] The presence of discontinuity and roughness on the trajectory has been found to correlate with a drastically increase of large jerk value reported in the past several decades. 27,28 Limiting the system maximum jerk value, which can diminish vibration influence motivated by the dominant vibration factor of the axis, reduce structure wear and resonance frequency emergence, improve tracking precision, and enhance trajectory smoothness and operational stability, is highly recommended to cope with the trajectory planning problem.…”

Section: Introductionmentioning

confidence: 99%

Minimum-jerk trajectory planning pertaining to a translational 3-degree-of-freedom parallel manipulator through piecewise quintic polynomials interpolation

Ding

2020

Advances in Mechanical Engineering

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This article aims to present a minimum-jerk trajectory planning approach to address the smooth trajectory generation problem of 3-prismatic-universal-universal translational parallel kinematic manipulator. First, comprehensive kinematics and dynamics characteristics of this 3-prismatic-universal-universal parallel kinematic manipulator are analyzed by virtue of the accepted link Jacobian matrices and proverbial virtual work principle. To satisfy indispensable continuity and smoothness requirements, the discretized piecewise quintic polynomials are employed to interpolate the sequence of joints’ angular position knots which are transformed from these predefined via-points in Cartesian space. Furthermore, the trajectory planning problem is directly converted into a constrained nonlinear multi-variables optimization problem of which objective function is to minimize the maximum of the joints’ angular jerk throughout the whole trajectory. Finally, two typical application simulations using the reliable sequential quadratic programming algorithm demonstrate that this proposed minimum-jerk trajectory planning approach is of explicit feasibility and appreciable effectiveness.

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“…In trajectory generation for industrial robots two families of trajectories, namely splines and polynomials, are often used. B-splines were used in [7] while fifth-degree polynomials were used in [8] for trajectory generation. However, in both cases the authors only considered the case when terminal velocities were zero.…”

Section: Introductionmentioning

confidence: 99%

Time-optimal parabolic interpolation with velocity, acceleration, and minimum-switch-time constraints

Lertkultanon

Pham

2016

Advanced Robotics

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A Minimum-Jerk Speed-Planning Algorithm for Coordinated Planning and Control of Automated Assembly Manufacturing

Cited by 15 publications

References 30 publications

Coverage of a Planar Point Set With Multiple Robots Subject to Geometric Constraints

Coverage of a Planar Point Set With Multiple Robots Subject to Geometric Constraints

Minimum-jerk trajectory planning pertaining to a translational 3-degree-of-freedom parallel manipulator through piecewise quintic polynomials interpolation

Time-optimal parabolic interpolation with velocity, acceleration, and minimum-switch-time constraints

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