Geometric Static Modeling Framework for Piecewise-Continuous Curved-Link Multi Point-of-Contact Tensegrity Robots

Abstract

Tensegrities synergistically combine tensile (cable) and rigid (link) elements to achieve structural integrity, making them lightweight, packable, and impact resistant. Consequently, they have high potential for locomotion in unstructured environments. This research presents geometric modeling of a Tensegrity eXploratory Robot (TeXploR) comprised of two semi-circular, curved links held together by 12 prestressed cables and actuated with an internal mass shifting along each link. This design allows for efficient rolling with stability (e.g., tip-over on an incline). However, the unique design poses static and dynamic modeling challenges given the discontinuous nature of the semi-circular, curved links, two changing points of contact with the surface plane, and instantaneous movement of the masses along the links. The robot is modeled using a geometric approach where the holonomic constraints confirm the experimentally observed four-state hybrid system, proving TeXploR rolls along one link while pivoting about the end of the other. It also identifies the quasi-static state transition boundaries that enable a continuous change in the robot states via internal mass shifting. This is the first time in literature a non-spherical two-point contact system is kinematically and geometrically modeled. Furthermore, the static solutions are closed-form and do not require numerical exploration of the solution. The MATLAB simulations are experimentally validated on a tetherless prototype with mean absolute error of 4.36°.

Figures (10)

• Figure 2: Two curved-link tensegrity robot, TeXploR, is structurally held together with 12 tensile cables. Change of robot pose is achieved through internal masses shifting along the curved links. At any instant in time, it has two points of contact with the ground.
• Figure 3: Geometric relationship the spatial $\{s\}$, body $\{b\}$ and link $\{1\},\{2\}$ coordinate systems. Here, $\{b\},\{1\}$ coincide and $\bm{z}_s$ is the normal to the surface of locomotion. The internal masses $P_i$ and ground contact points $Q_i$ along the links are denoted using $\theta_i,\phi_i$ respectively where $i=1,2$. The tangents $\bm{t}_i$ at the contact points lie along the surface.
• Figure 4: Four state hybrid system model of the TeXploR. The state transition is decided by the pivot and the rate of change of point of contact $\dot{\phi}_i$. During each state, the robot pivots about one of the ends of the curved links while rolling about the other.
• Figure 5: Different robot morphologies that can be modeled with the generalizable framework: (a) A two link prototype with a different shape and $T_{12}$. (b) A three curved-links resulting in three points of ground contact. (c) A two link prototype with arc length more than $180\degree$.
• Figure 6: The free-body diagram of TeXploR with the intertial and reaction forces.