Dynamic Point-to-Point Trajectory Planning Beyond the Static Workspace for Six-DOF Cable-Suspended Parallel Robots

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.

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Trajectory Planning of Cable-Suspended Parallel Robots Using Interval Positive-Definite Polynomials

Volume 4: 36th Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2012-71205 ◽

2012 ◽

Author(s):

Ping Ren ◽

Clément Gosselin

Keyword(s):

Trajectory Planning ◽

Inequality Constraints ◽

Positive Definite ◽

Parallel Robots ◽

Planning Problem ◽

Final States ◽

Time Duration ◽

Algebraic Investigation ◽

Point To Point ◽

Parametric Polynomials

In this paper, the dynamic point-to-point trajectory planning of cable-suspended robots is investigated. A simple planar two-degree-of-freedom (2-dof) robot is used to demonstrate the technique. In order to maintain the cables’ positive tension, a set of algebraic inequalities is derived from the dynamic model of the 2-dof robot. The trajectories are defined using parametric polynomials with the coefficients determined by the prescribed initial and final states, and the variable time duration. With the polynomials substituted into the inequality constraints, the planning problem is then converted into an algebraic investigation on how the coefficients of the polynomials will affect the number of real roots over a given interval. An analytical approach based on a polynomial’s Discrimination Matrix and Discriminant Sequence is proposed to solve the problem. It is shown that, by adjusting the time duration within appropriate ranges, it is possible to find positive-definite polynomials such that the polynomial-based trajectories always satisfy the inequality constraints of the dynamic system. Feasible dynamic trajectories that are able to travel both beyond and within the static workspace will exploit more potential of the cable-suspended robotic platform.

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