Dynamically Feasible Trajectories for Three-DOF Planar Cable-Suspended Parallel Robots

2014 ◽  
Author(s):  
Xiaoling Jiang ◽  
Clément Gosselin
Keyword(s):  
Natural Frequency ◽  
Trajectory Planning ◽  
Dynamic Modelling ◽  
Parallel Robots ◽  
Planning Approach ◽  
Planning Technique ◽  
Three Degree Of Freedom ◽  
Novel Applications ◽  
Translational Dynamic ◽  
Special Frequencies

This paper proposes a trajectory planning technique for planar three-degree-of-freedom cable-suspended parallel robots. Based on the kinematic and dynamic modelling of the architecture, force constraints that can guarantee that cables remain under tension are obtained. Periodic parametric trajectories that extend beyond the static workspace are designed. The trajectories involve combined translations and rotations. Substituting the trajectories into the force constraints, interval arithmetics is used to search for global conditions on the trajectory parameters which ensure that the trajectories are feasible. Special frequencies related to combined rotational and translational motions are exposed which can be used to better exploit cable-suspended robots. Moreover, it is observed that the special frequencies related to the translation are akin to the natural frequency of pendulum-like systems. The proposed trajectory planning approach can be used to plan combined rotational and translational dynamic trajectories that can extend beyond the static workspace of the mechanism, thereby opening novel applications and possibilities for cable-suspended robots.

Dynamic Point-To-Point Trajectory Planning for Three Degrees-of-Freedom Cable-Suspended Parallel Robots Using Rapidly Exploring Random Tree Search

2020 ◽  
Vol 12 (4) ◽  
Author(s):  
Sheng Xiang ◽  
Haibo Gao ◽  
Zhen Liu ◽  
Clément Gosselin
Keyword(s):  
Trajectory Planning ◽  
Degrees Of Freedom ◽  
Parallel Robots ◽  
Tree Search ◽  
Planning Techniques ◽  
Motion Primitive ◽  
Planning Technique ◽  
Point To Point ◽  
Three Degrees Of Freedom ◽  
Specific Distance

Abstract This paper proposes a dynamic point-to-point trajectory planning technique for three degrees-of-freedom (DOFs) cable-suspended parallel robots. The proposed technique is capable of generating feasible multiple-swing trajectories that reach points beyond the footprint of the robot. Tree search algorithms are used to automatically determine a sequence of intermediate points to enhance the versatility of the planning technique. To increase the efficiency of the tree search, a one-swing motion primitive and a steering motion primitive are designed based on the dynamic model of the robot. Closed-form expressions for the motion primitives are given, and a corresponding rapid feasibility check process is proposed. An energy-based metric is used to estimate the distance in the Cartesian space between two points of a dynamic point-to-point task, and this system’s specific distance metric speeds up the coverage. The proposed technique is evaluated using a series of Monte Carlo runs, and comparative statistics results are given. Several example trajectories are presented to illustrate the approach. The results are compared with those obtained with the existing state-of-the-art methods, and the proposed technique is shown to be more general compared to previous analytical planning techniques while generating smoother trajectories than traditional rapidly exploring randomized tree (RRT) methods.

Trajectory Planning of Projectile Catching Maneuvers for Robotic Manipulators

2018 ◽  
Author(s):  
Mark Charlet ◽  
Élodie Marcellini ◽  
Clément Gosselin
Keyword(s):  
Trajectory Planning ◽  
Polynomial Interpolation ◽  
Robotic Manipulators ◽  
Robotic Manipulator ◽  
Heuristic Approach ◽  
Robot Trajectory ◽  
Planning Approach ◽  
Planning Technique

This article introduces a trajectory planning approach for the catching of projectiles with a serial robotic manipulator. A description of the trajectory of the projectiles to be caught is first given. Then, a heuristic approach is introduced in order to determine the interception (catching) point. The planning of the robot trajectory that is required to reach the interception point with the proper velocity is then presented, based on polynomial interpolation. Finally, the trajectory of the robot used to decelerate and stop the projectile is planned. Examples of catching maneuvers are provided in order to illustrate the proposed trajectory planning technique.

Dynamic Modelling of a Three Degree-of-Freedom Planar Platform-Type Manipulator

1997 ◽  
Author(s):  
Hazem A. Attia ◽  
Maher G. Mohamed
Keyword(s):  
Differential Equations ◽  
Efficient Solution ◽  
Equations Of Motion ◽  
Translational Motion ◽  
Dynamic Modelling ◽  
Degree Of Freedom ◽  
Constraint Forces ◽  
Dynamic Formulation ◽  
System Of Particles ◽  
Three Degree Of Freedom

Abstract In this paper, the dynamic modelling of a planar three degree-of-freedom platform-type manipulator is presented. A kinematic analysis is carried out initially to evaluate the initial coordinates and velocities. The dynamic model of the manipulator is formulated using a two-step transformation. Initially, the dynamic formulation is written in terms of the Cartesian coordinates of a dynamically equivalent system of particles. Since there is no rotational motion associated with a particle, then the differential equations of motion are derived by applying Newton’s second law to study the translational motion of the particles. The constraint forces between the particles are expressed in terms of Lagrange multipliers. Then, the differential equations of motion are written in terms of the relative joint variables. This leads to an efficient solution and integration of the equations of motion. A numerical example is presented and a computer program is developed.

A Geodesic-Based Robot Trajectory Planning Approach for Cold Spray Applications

2019 ◽  
Vol 28 (5) ◽  
pp. 939-945 ◽  
Author(s):  
Zhenhua Cai ◽  
Xufeng Liang ◽  
Beigao Chen ◽  
Chunnian Zeng ◽  
Chen Chen ◽  
...  
Keyword(s):  
Cold Spray ◽  
Trajectory Planning ◽  
Robot Trajectory ◽  
Planning Approach ◽  
Robot Trajectory Planning ◽  
Spray Applications

3D Curve Generation Using Spherical Polar Piecewise Interpolation in CAD and CAM

2020 ◽  
Vol 896 ◽  
pp. 224-228
Author(s):  
Mihai Dupac
Keyword(s):  
Path Planning ◽  
Coordinate System ◽  
Numerical Simulations ◽  
Trajectory Planning ◽  
Robot Arm ◽  
Polar Plane ◽  
Spherical Coordinate ◽  
Manufacturing Efficiency ◽  
Planning Approach ◽  
Design And Manufacturing

In this paper a newly 3D path planning approach and curve generation for design and manufacturing efficiency is considered. The 3D path is generated by a combination of piecewise interpolating curves - along a given number of via-points - created via a spherical coordinate system specified by the polar angles, radial distances and the associated azimuthal angles. Each piecewise interpolating curve is constructed using Hermite polar interpolation in the projective polar plane and the rotating azimuthal plane. To verify the proposed approach, numerical simulations for the generation of a helix design, a 4 and 6 leaf design and a trajectory planning of a picking robot arm are conducted.

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