Scientists have long theorized that the cheetah’s tail contributes to its impressive maneuvrability at high speeds by stabilizing its body. This has inspired the design of several agile robots, including Dima - a wheeled platform that used cheetah-inspired inertial tail swings to better execute rapid acceleration and turning motions. Subsequent research suggests that the effectiveness of the cheetah’s tail might be enhanced by aerodynamic effects. In this paper, we introduce AeroDima: a follow-up to the original Dima design that uses aerodynamic drag on the tail as the primary mechanism for generating the stabilizing torque. The resulting sail-like tail is substantially lighter than the original, but still improves the performance of the platform, allowing it to enter turns at a higher speed without toppling. While the yaw rate of the robot was actually higher without the tail, the tail substantially reduced unwanted roll, confirming that this appendage increases maneuvrability by increasing stability, rather than by directly contributing to lateral acceleration.

With their combination of power and compliance, pneumatic actuators have great potential for enabling dynamic and agile behaviors in legged robots, but their complex dynam-ics impose control challenges that have hindered widespread use. In this paper, we describe the development of a tractable model and characterization procedure of an off-the-shelf double acting pneumatic cylinder controlled by on/off solenoid valves for use in trajectory optimization. With this we are able to generate motions which incorporate both the body and actuator dynamics of our robot Kemba: a novel quadrupedal robot prototype with a combination of electric and pneumatic actu-ators. We demonstrate both a 0.5 m jump and land maneuver, and a maximal 1 m jump, approximately 2.2 times its leg length, on the physical hardware with the proposed model and approach. The hardware matches the desired trajectory with a maximum height error of only 5 cm without any feedback on the pneumatic joints, demonstrating the utility of the model in high-level motion generation, and capability of the physical robot.

It has been shown that changing the coordinates describing a multi-body system to use absolute rather than relative angles produces a significant improvement in the tractability of trajectory optimization problems. This simplifies the equations of motion when modelling long kinematic chains. In this paper, we extend this idea by investigating whether a maximal coordinate system, which also describes the translational position of bodies using absolute coordinates, might lead to further performance improvements. We compare it to the relative translation, absolute orientation (RTAO) coordinate scheme using a batch of trajectory optimization trials selected with contact-implicit legged locomotion applications in mind. We find that maximal coordinates tend to shorten solving times for spatial problems, while the RTAO formulation still performs best in the case of planar motion.

Elaborate trajectory optimization models with many degrees of freedom can be a useful locomotion-planning tool, as they provide rich solutions that take advantage of the robot's specific morphology. They are, however, prone to falling into local minima. Depending on the seed that initializes the solver, the trajectories themselves and the extent to which they minimize the cost function can vary widely, making it impossible to judge the quality of any solution without generating many more. In this paper, we argue that this perceived drawback can actually be a powerful advantage in exploratory studies, since the resulting set of diverse motions can reveal which features tend to be associated with good performance, and therefore aid in the formulation of strategies for executing challenging maneuvers. We selected rapid gait termination from a high-speed gallop as our case study - a dangerous and scarcely-researched movement. By analyzing a set of over 3000 monopedal and quadrupedal trajectories, we were able to extract conclusions about how braking and sliding should be performed to reduce the stopping distance, and identify a hindlimb action that creates large braking forces.

An actuated spine appears to be a critical component for maneuverability in quadruped animals. However, robotic systems have yet to capitalize on this mechanism. This research compares three different spine morphologies in the planar case, namely the rigid, revolute and prismatic spine. Using a wide range of robots sampled from the design space (200 robots sampled at random), large-scale trajectory optimization (60 seed points per robot per spine morphology) was used to determine the best spine morphology in terms of stride averaged acceleration. Bootstrapping was performed on the results to achieve a better statistical representation and this revealed that for 75% of the robots, a prismatic spine design is the most effective at rapid acceleration, followed by the revolute spine at 6% and rigid spine at 18%.

For fast-moving legged robots, the ability to stop rapidly is essential if they are to move safely through unpredictable environments. There is a trade-off between stability and rapidity however, as the forces that slow the robot down also tend to cause a toppling moment. This paper examines how rapid deceleration motions performed on a bipedal robot are affected if it is forced to maintain zero rate of change in angular momentum (ZRAM) throughout the maneuver. By using trajectory optimization to generate over 4000 gait termination motions from speeds comparable to a sprinting human, it was found that the stopping distance could be reduced by 12% and time by 25% by relaxing the ZRAM condition, with greater reductions possible through the addition of a free stabilizing limb. The ability to moderate the pitch of the robot while decelerating was found to be paramount to achieving a rapid stop and thus, a template incorporating an inertial body and stabilizing appendages is proposed to represent these maneuvers.

This paper presents a novel approach to achieving aerial pitch righting in a mobile robot, inspired by the draglines used by jumping spiders. We developed and simulated a mathematical model of the spider during the aerial phase of its jump to gain further insight into the factors affecting the pitch response. The results demonstrate that the dragline could also potentially function as a brake, slowing the spider down before landing. Subsequently, we developed a small robotic platform to demonstrate dragline-based aerial pitch righting on a robot experimentally. Lastly, the possible size and weight advantages over other pitch righting methods are discussed.