Kinematics, Dynamics and Control of a Planar 3-DOF Tensegrity Robot Manipulator

Abstract

In this paper the kinematic and the dynamic analysis, and a nonlinear control strategy for a planar three-degree-of-freedom tensegrity robot manipulator are addressed. A geometric method is used to obtain the set of equations that describe the position analysis. Initially, solutions to the problems concerning forward and reverse kinematic analysis are presented; then, the forward velocity coefficients matrix is obtained analytically. The Lagrangian approach is used to deduce the dynamic equation of motion and its main properties are described using the nonlinear control system theory. Finally, a feedback-linearization-based nonlinear control scheme is applied to the mechanism to follow a prescribed path in the Cartesian coordinate system. The obtained results show that lightweight mechanisms which incorporate tensegrity systems could be used in a positioning problem.

Static and Stability Analysis of a Planar Compliant Tensegrity Mechanism

“…This is expected because when adding the third equation for C 1 into the system it made the Sylvester matrix in Eqn. (18) redundant, thus no stable solutions. However, the gap between 0 and 0.5 m for γ 1 and 0 and 1.5 m for γ 2 is unexpected and interesting to note.…”

“…The unique x 1 can be calculated by rearranging Eqn. (18) and substituting x 2 into the coefficients. Thereafter, unique values for γ 1 and γ 2 can be calculated for each x 1 and x 2 value from Eqn.…”

“…Moreover, the mechanism orientation may be controlled through its compliance, such as, by indirectly varying free lengths of the spring elements. Such modifications have been experimentally introduced to build tensegrity robots, however, their kinematic analysis has been limited [17][18][19][20]. The presented research analyzes the effect of variation of spring free lengths on the static equilibrium and stability of a planar tensegrity mechanism.…”

“…26)J i and K i are polynomials of x 2 to the 6th degree and are used to form a Sylvester matrix dependent only on x 2 , similar to how Eqn (18). was constructed for the previous case.…”

An advanced bionic knee joint mechanism with neural network controller

“…The lower limb rehabilitation training of several rehabilitation robots has been analyzed in Arsenault and Gosselin (2005, 2006a,b, 2009; Vasquez and Correa (2007); Murray et al (2015); Esquenazi and Talaty (2019); Nicholson-Smith et al (2020), and Muralidharan and Wenger (2021). Yet, these robots have not been analyzed from the perspective of bionics.…”