Design and control of compliant tensegrity robots through simulation and hardware validation

Abstract

To better understand the role of tensegrity structures in biological systems and their application to robotics, the Dynamic Tensegrity Robotics Lab at NASA Ames Research Center, Moffett Field, CA, USA, has developed and validated two software environments for the analysis, simulation and design of tensegrity robots. These tools, along with new control methodologies and the modular hardware components developed to validate them, are presented as a system for the design of actuated tensegrity structures. As evidenced from their appearance in many biological systems, tensegrity ('tensile-integrity') structures have unique physical properties that make them ideal for interaction with uncertain environments. Yet, these characteristics make design and control of bioinspired tensegrity robots extremely challenging. This work presents the progress our tools have made in tackling the design and control challenges of spherical tensegrity structures. We focus on this shape since it lends itself to rolling locomotion. The results of our analyses include multiple novel control approaches for mobility and terrain interaction of spherical tensegrity structures that have been tested in simulation. A hardware prototype of a spherical six-bar tensegrity, the Reservoir Compliant Tensegrity Robot, is used to empirically validate the accuracy of simulation.

Keywords: bioinspired locomotion; central pattern generators; compliant robotics; planetary exploration; soft robotics; tensegrity.

Figure 1.

Computer simulations of a nucleated tensegrity cell model exhibits mechanical coupling between the cell, the cytoskeleton and the nucleus. (Adapted from [2], with permission from Macmillan Publishers Ltd.) (Online version in colour.)

Figure 2.

Tensegrity models of the spine show how vertebrae float without touching. (Image courtesy of Tom Flemons. © copyright 2006 [7].)

Figure 3.

Mission scenario—a tightly packed set of tensegrities expands, spreads out, falls to the surface of the Moon and then safely bounces on impact. The same tensegrity structure cushioning landing is then used for exploration.

Figure 4.

ReCTeR: an untethered, highly compliant, spherical tensegrity robot. Top left: deployed robot. (Credit: NASA Ames/Eric James.) Centre right: active folding. Bottom: ReCTeR rolling from right to left.

Figure 5.

The various tensegrity configurations used in this paper. (a) Tensegrity icosahedron with only outer-shell members. (b) Tensegrity icosahedron with a payload by inner elements. (c) ReCTeR configuration with passive outer-shell and actuated spring–cable assemblies. (Online version in colour.)

Figure 6.

(a–d) Kinematic comparison of Euler–Lagrange (E-L) and NTRT simulators and ReCTeR motion capture data. (a) shows the experimental set-up. The rest length of two actuated spring–cable assemblies (dashed lines) is modified. The full range of tracked end-cap motion during the experiment is shown in transparent yellow (convex hull). The end caps indicated by small squares are on the ground. (b–d) show vertical displacement of the end cap indicated by the large black dot in (a) as a function of the lengths of the two actuated cables. The end cap where we trace the displacement is not directly actuated and is floating. The nodal displacement as a function of the actuator position is nonlinear, even for modest displacements. Note that the left-most point (0.05, 0.05, 0) is the reference point; displacements are relative to this initial state. (Online version in colour.)

Figure 7.

Comparing the dynamics of the robot and NTRT. The tensioned spring–cable assembly indicated by the dashed line is released (0.32–0.535 m at 0.6 m s⁻¹), causing the robot to topple. Two other actuated members are also tensioned, while the other three actuated springs are at their initial lengths, resulting in two slack springs. We observed a time-averaged error of the end caps' vertical positions of less than 5% of ReCTeR's diameter for all end caps. (Online version in colour.)

Figure 8.

Distance covered by the robot in 60 s with distributed learning of open-loop controllers based on coevolutionary algorithms. Each of the 24 outer-shell spring–cable assembly controllers has a different evolution pool, but their combined behaviour is optimized. (Online version in colour.)

Figure 9.

Regular icosahedron tensegrity shape with central payload (figure 5b). The highlighted contact surface with the ground creates a reaction force N (upwards arrow) that, at rest, balances the weight of the structure, represented on the figure by the downwards arrow mg. Torque is created on the whole structure when displacement of the centre of mass from its rest position occurs. (Online version in colour.)

Figure 10.

Computation of new rest lengths according to the spring–cable assemblies’ individual orientations v_i (time t^(n–1)). Length modification is indicated by coloured lines, dashed red if reduced and light green if elongated. The resulting effect is displacement of the central payload in the desired direction v (time ). (Online version in colour.)

Figure 11.

Trajectory of the tensegrity (top view). The dark curve represents the trajectory while the robot is driven by the reactive control algorithm and the CPG is in the learning mode (50 s). Motion is regular and the heading is maintained throughout the entire period. Light solid (yellow) and dashed (red) trajectories represent the path travelled once the CPG controller takes over (40 s). When the CPG is coupled to the height signal and receives inputs from the second-order inverse kinematics algorithm (dashed red curve), the resulting trajectory is a long and relatively straight line extending well the reactive control. (Online version in colour.)

Figure 12.

Examples of successful locomotion over complex terrains, such as slopes, bumps and obstacles. (Online version in colour.)

Figure 13.

Fast online learning of a static feedback controller for a Matsuoka oscillator on ReCTeR based on uncalibrated strain-gauge sensors. The top left plot shows the fraction of feed-forward versus feedback control. During learning, both feedback and feed-forward controllers (training signals) are active. The influence of the open-loop feed-forward controller decreases, and when its fraction is below 0.2, learning stops and only the trained feedback controller is active. The left plot on the second row shows vertical coordinates (in millimetres) of the four end caps with the largest vertical displacements as a function of time. The five surrounding plots are details of this plot, showing different training and testing phases. (a) Fully open-loop control. (b) Switch from partially open-loop and feedback control to full feedback control, learning stops. (c) We perturb the robot by pushing it down, preventing all movements. (d) The feedback controller recovers after the robot was lifted from the ground. (e) Behaviour of the robot after 250 s (170 s closed loop).