Edward L. Zhu

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.

Xu Shen, Edward L. Zhu, Yvonne R. Stürz et al.

We present a hierarchical control approach for maneuvering an autonomous vehicle (AV) in tightly-constrained environments where other moving AVs and/or human driven vehicles are present. A two-level hierarchy is proposed: a high-level data-driven strategy predictor and a lower-level model-based feedback controller. The strategy predictor maps an encoding of a dynamic environment to a set of high-level strategies via a neural network. Depending on the selected strategy, a set of time-varying hyperplanes in the AV's position space is generated online and the corresponding halfspace constraints are included in a lower-level model-based receding horizon controller. These strategy-dependent constraints drive the vehicle towards areas where it is likely to remain feasible. Moreover, the predicted strategy also informs switching between a discrete set of policies, which allows for more conservative behavior when prediction confidence is low. We demonstrate the effectiveness of the proposed data-driven hierarchical control framework in a two-car collision avoidance scenario through simulations and experiments on a 1/10 scale autonomous car platform where the strategy-guided approach outperforms a model predictive control baseline in both cases.

Edward L. Zhu, Yvonne R. Stürz, Ugo Rosolia et al.

We present a decentralized minimum-time trajectory optimization scheme based on learning model predictive control for multi-agent systems with nonlinear decoupled dynamics and coupled state constraints. By performing the same task iteratively, data from previous task executions is used to construct and improve local time-varying safe sets and an approximate value function. These are used in a decoupled MPC problem as terminal sets and terminal cost functions. Our framework results in a decentralized controller, which requires no communication between agents over each iteration of task execution, and guarantees persistent feasibility, finite-time closed-loop convergence, and non-decreasing performance of the global system over task iterations. Numerical experiments of a multi-vehicle collision avoidance scenario demonstrate the effectiveness of the proposed scheme.

Andrew P. Sabelhaus, Shirley Huajing Zhao, Mallory C. Daly et al.

The Underactuated Lightweight Tensegrity Robotic Assistive Spine (ULTRA Spine) project is an ongoing effort to develop a flexible, actuated backbone for quadruped robots. In this work, model-predictive control is used to track a trajectory in the robot's state space, in simulation. The state trajectory used here corresponds to a bending motion of the spine, with translations and rotations of the moving vertebrae. Two different controllers are presented in this work: one that does not use a reference input but includes smoothing constrants, and a second one that uses a reference input without smoothing. For the smoothing controller, without reference inputs, the error converges to zero, while the simpler-to-tune controller with an input reference shows small errors but not complete convergence. It is expected that this controller will converge as it is improved further.

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.