This paper studies a generally applicable, sensitive, and intuitive error metric for the assessment of robotic swarm density controller performance. Inspired by vortex blob numerical methods, it overcomes the shortcomings of a common strategy based on discretization, and unifies other continuous notions of coverage. We present two benchmarks against which to compare the error metric value of a given swarm configuration: non-trivial bounds on the error metric, and the probability density function of the error metric when robot positions are sampled at random from the target swarm distribution. We give rigorous results that this probability density function of the error metric obeys a central limit theorem, allowing for more efficient numerical approximation. For both of these benchmarks, we present supporting theory, computation methodology, examples, and MATLAB implementation code.

Embedding the dynamics of the Spring Loaded Inverted Pendulum (SLIP) and applying a compositional controller around it can simplify dynamic legged robot locomotion control, but what is the energetic cost of this convenience? This paper measures the magnitude of this effect in such a way that the results are applicable to a wide class of jumping robots. A three-link monoped model with revolute joints is used to compare the energetic costs of locomotion using two different control approaches: 1) SLIP-embedding with a Raibert-style controller optimized for energetic efficiency, and 2) a trajectory optimized only for energetic efficiency. By performing this comparison in simulation for a large number of different monopeds randomly sampled from a space of realistic robot designs, it is found that the SLIP-Raibert approach requires, on average, almost twice the energy of the trajectory-optimized controller to traverse a given distance. Furthermore, the increase in energetic cost does not depend much on the particulars of the robot design, as the SLIP-Raibert approach requires at least 50% more energy for approximately 88% of realistic robot designs.

This paper explores a stochastic approach for controlling swarms of independent robots toward a target distribution in a bounded domain. The robot swarm has no central controller, and individual robots lack both communication and localization capabilities. Robots can only measure a scalar field (e.g. concentration of a chemical) from the environment and from this deduce the desired local swarm density. Based on this value, each robot follows a simple control law that causes the swarm as a whole to diffuse toward the target distribution. Using a new holonomic drive robot, we present the first confirmation of this control law with physical experiment. Despite deviations from assumptions underpinning the theory, the swarm achieves the theorized convergence to the target distribution in both simulation and experiment. In fact, simulated and experimental performance agree with one another and with our hypothesis that the error from the target distribution is inversely proportional to the square root of the number of robots. This is evidence that the algorithm is both practical and easily scalable to large swarms.

Animals use tails to improve locomotion performance; here we assess how the biomimetic MIT Cheetah robot can do the same. Analysis proves that for a given power and weight, tails can provide greater average torque than reaction wheels for the short times of interest in high speed running. A simple tail controller enables the cheetah to perform aerial orientation maneuvers in simulation. The MIT Cheetah robot's tail rejects an impulsive disturbance from a `wrecking ball' in experiments. This study demonstrates that a tail will help the MIT Cheetah achieve its goal of 30mph locomotion by 2014.

Swing-leg retraction was introduced as a way to improve the stability and disturbance rejection of running robots. It was also suggested that the reduced foot speed due to swing-leg retraction can help reduce impact energy losses, decrease peak forces, and minimize foot slipping. However, the extent to which swing-leg retraction rate influences all these benefits was unknown. In this paper, we present a study on the effect of swing-leg retraction rate on these benefits. The results of this study show that swing-leg retraction can indeed improve the performance of running robots in all of the suggested areas. However, the results also show that, for moderate and high running speeds, the optimal retraction rate for maximal disturbance rejection and stability is different from the optimal retraction rate for minimal impact losses, peak forces, and foot slipping. This discrepancy indicates an inherent tradeoff to consider when selecting the retraction rate for a robot control system: in general, retraction rate can be optimized for better stability and disturbance rejection or for more favorable efficiency, impact forces, and footing stability, but not all simultaneously. Furthermore, this tradeoff becomes more severe as running speed increases.

Swing leg retraction reduces touchdown energy losses of running by decreasing foot speed at the moment of ground contact, but does the additional acceleration of the swing leg cost more energy than is saved? To determine whether swing leg retraction can increase the overall energy efficiency of running robots, we find the optimally efficient gaits of a McGeer-like runner over a range of retraction rates. Results show that overall energy usage, including that used to swing the legs, scales with energy loss at touchdown, which is minimized at the retraction rate that zeros foot tangential speed at ground contact. Other benefits of swing leg retraction, such as reduced foot slippage and damaging touchdown forces, are realized simultaneously with optimal energy efficiency.