Trajectory Planning for a 3-SPS-U Tensegrity Mechanism

Abstract

This article presents the actuation strategy of a 2-DOF tensegrity type mechanism that employs three tension springs and a passive universal joint. This mechanism is proposed to be incorporated as an articulation unit for a piping inspection robot in order to overcome pipe bends and junctions. In the event of a junction, external actuations are required to allow the mechanism as well as the robot to follow a certain direction. Using DC-motors coupled with encoders, experiments are carried out on a test bench of the tensegrity mechanism. The actuation of the mobile platform is performed using cables that pass through each spring. By correlating the architecture to a 3-SPS-U parallel mechanism, the singularity-free workspace of the mechanism is analyzed to identify the tilt limits. A closed-loop PID controller is implemented using a microcomputer to perform a linear trajectory within the singularity-free workspace. The Inverse Kinematic Problem (IKP) is solved by passing input tilt angles to the controller. With the help of a force control algorithm, the experiments are carried out under no-load conditions for vertical and horizontal orientations of the mechanism. The error data of the joint positions and the motor torques are then interpreted for both orientations of the mechanism.

Mapping the Tilt and Torsion Angles for a 3-SPS-U Parallel Mechanism

“…The actual prototype that will be incorporated with the piping-inspection robot has the design parameters r f as 11 mm and h = 0.6 [16]. As an experimental validation is carried out in the upcoming section, a scaled value of r f = 56.7 mm for h = 0.6 is chosen for the singularity analysis [25]. As the constraint equations require joint limits for analysis, the minimum and maximum lengths for each prismatic spring are set as l min = 40 mm and l max = 106 mm.…”

“…This actuation is carried out through the cables that pass through the springs of the mechanism. The pose variables and the articular variables for the mechanism are given by q = [η, φ] and ρ = [l 1 , l 2 , l 3 ] [25]. The length of the springs is calculated using Equations (16a)-(16c) in the Euler space.…”

Design and Analysis of a Series-Parallel Hybrid 3-SPS-U Mechanism

“…Thus, a control law will be implemented which takes into account the friction and cable elasticity factors similar to the control strategy of a tensegrity structure proposed by Fasquelle et al [25]. Also, advanced controllers such as the EtherCAT will be employed for the experiments when compared to a simple BeagleBone black card that was employed for the single-stage model in [21]. The EtherCAT allows controlling several components at the same time from a central unit.…”

“…The Type-3 singularities occur only when there exist both serial and parallel singularities, which is once again not possible for the mechanism. Based on the experiments conducted on the tensegrity mechanism in [21], it was observed that one or two of the prismatic springs reach their minimum length at two specific positions referred to as:…”

“…It has to be noted that a common azimuth for the entire assembly assuming that there exists no friction between each module and the connecting elements. The experimental setup will then be validated in the future and the actuation strategy will follow a similar approach that was presented in [21]. An overview of the experimental platform developed at LS2N, France is shown in Fig.…”