Adrian K. Agogino

Andrew P. Sabelhaus, Huajing Zhao, Edward L. Zhu et al.

Robots with flexible spines based on tensegrity structures have potential advantages over traditional designs with rigid torsos. However, these robots can be difficult to control due to their high-dimensional nonlinear dynamics and actuator constraints. This work presents two controllers for tensegrity spine robots, using model-predictive control (MPC) and inverse statics optimization. The controllers introduce two different approaches to making the control problem computationally tractable. The first utilizes smoothing terms in the MPC problem. The second uses a new inverse statics optimization algorithm, which gives the first feasible solutions to the problem for certain tensegrity robots, to generate reference input trajectories in combination with MPC. Tracking the inverse statics reference input trajectory significantly reduces the number of tuning parameters. The controllers are validated against simulations of two-dimensional and three-dimensional tensegrity spines. Both approaches show noise insensitivity and low tracking error, and can be used for different control goals. The results here demonstrate the first closed-loop control of such structures.

Andrew P. Sabelhaus, Albert H. Li, Kimberly A. Sover et al.

Robots built from cable-driven tensegrity (`tension-integrity') structures have many of the advantages of soft robots, such as flexibility and robustness, while still obeying simple statics and dynamics models. However, existing tensegrity modeling approaches cannot natively describe robots with arbitrary rigid bodies in their tension network. This work presents a method to calculate the cable tensions in static equilibrium for such tensegrity robots, here defined as compound tensegrity. First, a static equilibrium model for compound tensegrity robots is reformulated from the standard force density method used with other tensegrity structures. Next, we pose the problem of calculating tension forces in the robot's cables under our proposed model. A solution is proposed as a quadratic optimization problem with practical constraints. Simulations illustrate how this inverse statics optimization problem can be used for both the design and control of two different compound tensegrity applications: a spine robot and a quadruped robot built from that spine. Finally, we verify the accuracy of the inverse statics model through a hardware experiment, demonstrating the feasibility of low-error open-loop control using our proposed methodology.

Andrew P. Sabelhaus, Lara Janse van Vuuren, Ankita Joshi et al.

Walking quadruped robots face challenges in positioning their feet and lifting their legs during gait cycles over uneven terrain. The robot Laika is under development as a quadruped with a flexible, actuated spine designed to assist with foot movement and balance during these gaits. This paper presents the first set of hardware designs for the spine of Laika, a physical prototype of those designs, and tests in both hardware and simulations that show the prototype's capabilities. Laika's spine is a tensegrity structure, used for its advantages with weight and force distribution, and represents the first working prototype of a tensegrity spine for a quadruped robot. The spine bends by adjusting the lengths of the cables that separate its vertebrae, and twists using an actuated rotating vertebra at its center. The current prototype of Laika has stiff legs attached to the spine, and is used as a test setup for evaluation of the spine itself. This work shows the advantages of Laika's spine by demonstrating the spine lifting each of the robot's four feet, both as a form of balancing and as a precursor for a walking gait. These foot motions, using specific combinations of bending and rotation movements of the spine, are measured in both simulation and hardware experiments. Hardware data are used to calibrate the simulations, such that the simulations can be used for control of balancing or gait cycles in the future. Future work will attach actuated legs to Laika's spine, and examine balancing and gait cycles when combined with leg movements.

Lee-Huang Chen, Brian Cera, Edward L. Zhu et al.

This paper presents a new teleoperated spherical tensegrity robot capable of performing locomotion on steep inclined surfaces. With a novel control scheme centered around the simultaneous actuation of multiple cables, the robot demonstrates robust climbing on inclined surfaces in hardware experiments and speeds significantly faster than previous spherical tensegrity models. This robot is an improvement over other iterations in the TT-series and the first tensegrity to achieve reliable locomotion on inclined surfaces of up to 24\degree. We analyze locomotion in simulation and hardware under single and multi-cable actuation, and introduce two novel multi-cable actuation policies, suited for steep incline climbing and speed, respectively. We propose compelling justifications for the increased dynamic ability of the robot and motivate development of optimization algorithms able to take advantage of the robot's increased control authority.