Robust Planning for Dynamic Tensegrity Structures

Tensegrity Background

Tensegrity, i.e., tensional integrity, is an exciting structural principle for developing impact-tolerant and lightweight planetary rovers, which can achieve arbitrary forms and locomotion gaits. Contrary to traditional robot designs, rigid elements are not directly attached to one another, but instead are interconnected with a series of cables. Tensegrity designs were first popularized in architecture, but if the cables connecting these rigid parts are actuated to shorten or lengthen, it is now a reconfigurable robot.

These platforms can effectively adapt to highly unstructured environments, such as uneven terrain at space exploration destinations. In addition, tensegrity platforms are highly modular, resulting in cheaper, lighter, and mass-producible components. This is especially important for space exploration since increased weight requires more fuel during a launch, which leads to higher costs.


Nevertheless, controlling tensegrity robots with traditional methods is challenging due to the high dimensionality and nonlinearity of their dynamics, especially when combined with numerous sources of uncertainty. As a result, most existing solutions limit the depth to which the underlying dynamics are considered and provide only quasi-static paths, or discrete waypoints that can be reached with minimal dynamics. Conversely, embracing the underlying dynamics in the control process can enable desirable classes of motion, such as tumbling and bouncing, thus expanding platform mobility.

Project Objective

This project aims to provide new algorithmic, mathematical, and software tools to meet the challenges outlined above and provide dynamically feasible trajectories for purposeful long-term navigation of tensegrity robots in uneven terrain. The focus is on advancing the state-of-the-art in kinodynamic planning for high-dimensional robots with significant uncertainty, especially for applications involving soft contacts between a tensegrity structure and a highly unstructured surface environment. Computational efficiency is a crucial priority, as is a formal foundation for characterizing the robustness of the computed trajectories. Solutions will be evaluated first in physics-based simulation and then on real tensegrity platforms that are of interest to NASA, namely the icosahedron-shaped "SUPERball" rover, which is shown in the figure above.

Progress in Trajectory Planning for Tensegrity Rovers

Purposeful motion planning requires a global approach, where reasoning is conducted over long horizons and in accordance with terrain variability and operational objectives. Among the various classes of motion planning algorithms, sampling-based methods are accommodating of high dimensionality, which is exhibited by tensegrity systems. Some of these methods are also applicable for planning fully kinodynamic motion, where links between sampled configurations account for the full dynamic state, including velocities. Lastly, the complex effects of contact friction with rough terrain and obstacles can only be accurately simulated through the use of a physics engine.

We have achieved a fundamental demonstration of global motion planning for NASA's SUPERball rover by integrating the Stable Sparse RRT (SST) planner with the NASA Tensegrity Robotics Toolkit (NTRT). SST relaxes computing demands when planning for systems with complex dynamics through careful moderation of states that are explored and stored, thus achieving good path quality; NTRT provides a realistic simulation of the highly-coupled structural dynamics of tensegrity-based robots and their environmental interactions. An example trajectory produced from the combination of these tools is shown below:

This result exhibits the flexibility and effectiveness of the SST algorithm and the SUPERball tensegrity robot itself. The large 24-dimensional control space, however, results in a high computational cost. To bring planning demands more in line with the thrift of the physical platform, ongoing work will seek to simplify the control scheme and thus reduce its dimensionality while retaining the ability to produce diverse and effective motions. Instead of considering all inputs as independent, analysis and learning methods will be combined to produce motion primitives for changing the system's overall shape and momentum in various ways as well as for initiating and sustaining specific behaviors such as rolling and crawling gaits. A library of such maneuvers would serve as a much smaller control space to explore, potentially cutting execution time by orders of magnitude. Modifications to SST will also be considered that aim to focus its search toward the most useful parts of the environment.

Towards Planning under Uncertainty for Tensegrity Rovers

The difficulty of motion planning for tensegrity-based robots is further compounded by noisy actuation of controls, uncertainty about the state of the robot and about the terrain on which it operates, and inevitably imperfect modeling of system dynamics. Strong nonlinearities prevent these errors from being negated in a straightforward manner.

One strategy for minimizing the impact of uncertainty upon performance is to plan within belief-space, where the robot's state is represented probabilistically and a single control policy maps to a range of possible outcomes. Nonlinearity of error propagation may also be accounted for by utilizing a particle-based representation, which is capable of conforming to multi-modal probability distributions, instead of the standard but relatively inflexible Gaussian distribution. In the following image, several possible trajectories resulting from a single plan executed from an uncertain initial state are shown by superimposed transparent snapshots of SUPERball, with the nominal path shown as opaque. Due to accumulation of error, the disparity between these trajectories increases as the plan is executed.

Nevertheless, as with the previously discussed problem of trajectory planning, a drastic reduction in computational demand is necessary to make planning feasible under reasonable hardware limitations. The issue is that simulating motion for each sample of a particle set rapidly becomes a burdensome task. One potential work-around is to apply learning to develop stochastic models for the evolution of such a particle set, possibly facilitating accurate uncertainty propagation at a much-reduced sample count. Alternatively, planning conducted with a specific library of maneuvers and gaits could leverage information about the general stability or instability of these control strategies on various classes of terrain and perhaps incorporate feedback control to actively maintain specific gaits as perturbations are absorbed from the landscape.

Learning and Optimization

Prior work on tensegrity-based systems have demonstrated the success of bioinspired control strategies, which aim to identify a lower-dimensional control space to operate over. Among these methods, Central Pattern Generators (CPGs) are quite popular. A CPG reduces the high-dimensional control problem to a much lower dimension by constraining the controls propagated to the system to be rhythmic and oscillatory with respect to time. The resulting gaits' effectiveness in producing locomotion for the system is highly dependent on the architecture of the CPG network imposed on the system. Once a reasonable architecture for a system has been defined, we can search the much lower dimensional parameter space of the CPG system in order to find useful gaits for the system.

Applying these gaits to improve the efficiency of planning in the original system's control space can be achieved in a variety of ways. In the most straightforward application, we can treat our "learned" gaits as a dictionary of maneuvers, computing motion plans that consist of the application of these learned gaits over varying amounts of time in order to reach the goal. In more complex situations when movement may be more constrained due to the presence of obstacles or difficult terrain, instead of discrete parameter settings we can learn distributions over the CPG parameters and use these to bias our search for feasible motion plans. The latter approach allows for novel behavior exploration when forward progress is constrained, while also fully leveraging the learned effects of CPG parameter settings. Additionally, we can search the lower dimensional CPG parameter space much more efficiently than the full system's control space.

Current questions being addressed in this line of research include: (1) How to determine a reasonable network structure for the CPG in a more automated and data-driven way, (2) How to best identify which situations will benefit from the learned parameter distributions, and to adapt on-line our strategy as to when and to what degree to bias our search, (3) Using Bayesian optimization to minimize the number of trials needed to find a sufficient variety of successful CPG parameter settings for a given system.

Related Publications


This work has been supported by:

  • NASA Space Technology Research Fellowship NNX13AL71H awarded to Zakary Littlefield
  • NASA Early Career Faculty grant NNX15AU47G awarded to Kostas Bekris

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