Bezier Curve Based Programmed Trajectory for Coordinated Motion of Two Robots in Cartesian Space

Coordinated motion of two robots in Cartesian space is considered in the paper. The goal is to generate trajectories for which change of distance between points on trajectories during motion is minimal. To minimize relative position errors along trajectories an idea of corrective motion is introduced. Trajectory coordinates are calculated as the sum of programmed and corrective motions. To calculate the speed vector of the programmed motion at the current position, the speed at the closest point on the programmed trajectory is used. The closest point is defined as the one to which the distance from the current position is minimal or the programmed position at given time. In order to attract the generated trajectory to the programmed one a modification of the programmed speed vector is proposed. The described approach is verified in simulation. For simulation experiments programmed trajectories defined by Bezier curve segments are used. Simulations for different shapes of programmed trajectories and different programmed velocity rates are presented.

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An Algorithm for Generation of Coordinated Robot Trajectories in Cartesian Space

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.196.169 ◽

2013 ◽

Vol 196 ◽

pp. 169-180 ◽

Cited By ~ 3

Author(s):

Adam Słota

Keyword(s):

Virtual Environment ◽

Relative Position ◽

Accuracy Analysis ◽

Simulation Environment ◽

Coordinated Motion ◽

Generation Algorithm ◽

Cartesian Space ◽

Position And Orientation ◽

End Effectors ◽

Trajectory Generation Algorithm

In the paper a trajectory generation algorithm for two robots’ coordinated motion is presented. Two instances of the algorithm, each for one robot, run in the same time and calculate trajectories’ position and orientation coordinates. Initial and end robots’ end-effectors poses are defined and values of linear and angular speeds are programmed. To minimize relative position and orientation errors an idea of corrective motion is introduced. Trajectory coordinates are calculated as the sum of programmed and corrective motion. The algorithm was implemented in a simulation environment and results of simulation are presented. Static accuracy analysis for general case and stability verification for fixed values of robots’ parameters are described. Finally, an outline of proposed procedure of building a virtual environment for reachability verification and collision checking is presented.

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Motion Coordination of Two Robots in Cartesian Space Based on Mechanical Impedance

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.613.53 ◽

2014 ◽

Vol 613 ◽

pp. 53-59 ◽

Cited By ~ 1

Author(s):

Adam Slota

Keyword(s):

Mechanical Impedance ◽

Interaction Force ◽

Linear Increase ◽

Dimensional Case ◽

Motion Coordination ◽

Coordinated Motion ◽

Simulation Experiments ◽

Cartesian Space ◽

Motion Speed ◽

In Series

Coordinated motion of two robots in Cartesian space is considered in the paper. Coordinated trajectory is generated as the sum of two motions: programmed and corrective. The corrective motion aims at limitation of the interaction force between robots. For calculation of the corrective motion speed the idea of mechanical impedance is used. As a measure of force interactions between robots change of distance between robots TCPs is used. Simulation experiments carried out for one dimensional case show that application of impedance based correctors results in the linear growth of change of distance between robots TCPs for constant difference between robots programmed speeds. Thus a modification of impedance based correctors is proposed. The modification consists in introduction of an integrating element in series with impedance corrector. Simulation tests for the modified correctors provide improved results – magnitude of change of distance is decreased. Linear increase of change of distance for impedance corrector is changed into a constant non zero value, whereas constant non zero value is changed into zero value. Simulation results for two dimensional case of coordinated motion are also presented.

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Trajectory Planning with Bezier Curve in Cartesian Space for Industrial Gluing Robot

Intelligent Robotics and Applications - Lecture Notes in Computer Science ◽

10.1007/978-3-319-13963-0_15 ◽

2014 ◽

pp. 146-154 ◽

Cited By ~ 5

Author(s):

Zhijie Xu ◽

Shuai Wei ◽

Nianfeng Wang ◽

Xianmin Zhang

Keyword(s):

Trajectory Planning ◽

Bézier Curve ◽

Bezier Curve ◽

Cartesian Space

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A NURBS transition between a Bézier curve and its control polygon

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2021.113626 ◽

2021 ◽

pp. 113626

Author(s):

Imre Juhász

Keyword(s):

Bézier Curve ◽

Bezier Curve ◽

Control Polygon

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Optimal Bezier Curve Modification Function for Contrast Degraded Images

IEEE Transactions on Instrumentation and Measurement ◽

10.1109/tim.2021.3073320 ◽

2021 ◽

Vol 70 ◽

pp. 1-10

Author(s):

Bharath Subramani ◽

Ashish Kumar Bhandari ◽

Magudeeswaran Veluchamy

Keyword(s):

Bézier Curve ◽

Bezier Curve ◽

Degraded Images

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Automatic Lane-Changing Decision Based on Single-Step Dynamic Game with Incomplete Information and Collision-Free Path Planning

Actuators ◽

10.3390/act10080173 ◽

2021 ◽

Vol 10 (8) ◽

pp. 173

Author(s):

Hongbo Wang ◽

Shihan Xu ◽

Longze Deng

Keyword(s):

Path Planning ◽

Dynamic Game ◽

Single Step ◽

Bézier Curve ◽

Vehicle Safety ◽

Bezier Curve ◽

Lane Change ◽

Hardware In The Loop ◽

Power Performance ◽

Lane Changing

Traffic accidents are often caused by improper lane changes. Although the safety of lane-changing has attracted extensive attention in the vehicle and traffic fields, there are few studies considering the lateral comfort of vehicle users in lane-changing decision-making. Lane-changing decision-making by single-step dynamic game with incomplete information and path planning based on Bézier curve are proposed in this paper to coordinate vehicle lane-changing performance from safety payoff, velocity payoff, and comfort payoff. First, the lane-changing safety distance which is improved by collecting lane-changing data through simulated driving, and lane-changing time obtained by Bézier curve path planning are introduced into the game payoff, so that the selection of the lane-changing start time considers the vehicle safety, power performance and passenger comfort of the lane-changing process. Second, the lane-changing path without collision to the forward vehicle is obtained through the constrained Bézier curve, and the Bézier curve is further constrained to obtain a smoother lane-changing path. The path tracking sliding mode controller of front wheel angle compensation by radical basis function neural network is designed. Finally, the model in the loop simulation and the hardware in the loop experiment are carried out to verify the advantages of the proposed method. The results of three lane-changing conditions designed in the hardware in the loop experiment show that the vehicle safety, power performance, and passenger comfort of the vehicle controlled by the proposed method are better than that of human drivers in discretionary lane change and mandatory lane change scenarios.

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