Millimeter-wave (mmWave) point-cloud radar shows great promise in enabling responsive human-machine interfaces (e.g., through pose and gesture tracking and for emerging augmented reality approaches). However, generating dense and temporally consistent 3D human point clouds from sequential mmWave signals is challenging due to point-cloud sparsity, jitter, and noise. Existing approaches have made progress in single-frame densification, but are inaccurate over multiple frames. This work redefines the problem as a 3D point cloud denoising task, leveraging reverse diffusion processes to transform sparse mmWave data into detailed and accurate whole-body representations. Our proposed method, mmDiffusion, effectively exploits diffusion models and temporal context within mmWave sequences to learn the denoising process, resulting in denser and temporally coherent human point clouds. For the first time, we also introduce an evaluation metric tailored to measure temporal consistency for sequential 3D human point clouds. Experimental results demonstrate that mmDiffusion significantly outperforms existing methods.

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.

This paper introduces a framework for monocular 3D reconstruction of cheetah movements, leveraging a combination of data-driven and physics-based modeling as well as trajectory optimization. Unlike traditional methods that rely solely on kinematics, our approach integrates dynamic motion principles, enhancing the plausibility and generalization of motion estimates. Validated on the cheetah running dataset, AcinoSet, we achieve mean per-joint position errors of 78.8 mm and 72.5 mm, showcasing significant advancements over the existing model used in AcinoSet. By addressing the challenge of absent ground truth data, this work not only advances animal motion capture techniques but also informs the development of bio-inspired robotic systems, offering a robust solution for accurately capturing complex animal locomotion in natural settings.

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.

Tracking the 3D motion of agile animals in the wild will enable new insight into the design of robotic controllers. However, in-field 3D pose estimation of high-speed wildlife such as cheetahs is still a challenge [1]. In this work, we aim to solve two of these challenges: unnatural pose estimates during highly occluded sequences and synchronization error between multi-view data. We expand on our previous Full Trajectory Estimation (FTE) method with two significant additions: Pairwise FTE (PW-FTE) and Shutter-delay FTE (SD-FTE). The PW-FTE expands on image-dependent pairwise terms, produced by a convolutional neural network (CNN), to infer occluded 2D keypoints, while SD-FTE uses shutter delay estimation to correct the synchronization error. Lastly, we combine both methods into PW-SD-FTE and perform a quantitative and qualitative analysis on a subset of AcinoSet, the video dataset of rapid and agile motions of cheetahs. We found that SD-FTE has significant benefits in tracking the position of the cheetah in the world frame, while PW-FTE provided a more robust 3D pose estimate during events of high occlusion. The PW-SD-FTE was found to retain both advantages, resulting in an improved baseline for AcinoSet. Code and data can be found at https://github.com/African-Robotics-Unit/AcinoSet/tree/pw_sd_fte.

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.

For robots to leave the safety of the laboratory and explore the world, maneuverability will need to be mastered. However, transient motions, such as rapid acceleration and deceleration, have received little attention in the literature. This is mainly due to the complexity of analyzing these high dimensional systems that have no closed-form solution which makes controller design a non-trivial task. One method is to utilize heuristic control inspired by animal locomotion (or intuition), but these may not be optimal for a given task. Here, we take the novel approach and leverage trajectory optimization methods to enable us to identify heuristic controllers for the task of transient locomotion. Specifically, we investigate acceleration to a steady-state gait as well as decelerating from a steady-state gait to rest. These identified heuristic controllers were then validated on a hybrid pneumatic-electric monopod robot. Our initial results indicate that a Raibert controller is in fact the energy optimal policy for transient maneuvers.

Animals are capable of extreme agility, yet understanding their complex dynamics, which have ecological, biomechanical and evolutionary implications, remains challenging. Being able to study this incredible agility will be critical for the development of next-generation autonomous legged robots. In particular, the cheetah (acinonyx jubatus) is supremely fast and maneuverable, yet quantifying its wholebody 3D kinematic data during locomotion in the wild remains a challenge, even with new deep learning-based methods. In this work we present an extensive dataset of free-running cheetahs in the wild, called AcinoSet, that contains 119, 490 frames of multi-view synchronized high-speed video footage, camera calibration files and 7, 588 human-annotated frames. We utilize markerless animal pose estimation to provide 2D keypoints. Then, we use three methods that serve as strong baselines for 3D pose estimation tool development: traditional sparse bundle adjustment, an Extended Kalman Filter, and a trajectory optimization-based method we call Full Trajectory Estimation. The resulting 3D trajectories, human-checked 3D ground truth, and an interactive tool to inspect the data is also provided. We believe this dataset will be useful for a diverse range of fields such as ecology, neuroscience, robotics, biomechanics as well as computer vision. Code and data can be found at: https://github.com/African-Robotics-Unit/AcinoSet.

Many agile legged animals employ lightweight, furry tails to regulate orientation during running, leaping, and turning. Most robots attempting the same tasks either lack a tail or employ one with high inertia, which can induce impractical payload and energy costs. Inspired by nature's solution to this tradeoff, we explore the use of aerodynamic drag tails in reorientation tasks. In this article, we present a model of the aerodynamic drag and from this derive a metric that allows for direct comparison between aerodynamic and inertial tails. Motivated by this model, we construct a tail to maximize this effectiveness while minimizing inertia. We demonstrate the utility of this tail for two dynamic behaviors executed on a quadrupedal robot. First, in aerial reorientation the robot achieves a 90°rotation within one body length of fall at the same performance as an inertial tail but with just 37% of the normalized inertia. Second, the forward acceleration of the robot is improved by 12% despite increasing the system mass by 10% over a tailless version. These results show that aerodynamic drag can provide significant control authority for a robot while decreasing the payload and energy cost.

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.

The natural world hosts a few mammals that display both a high degree of agility and speed. However these animals have complex leg morphologies. Robot designers are thus faced with the dilemma of which morphology to employ when designing the next generation of agile legged robots. Thus this letter presents a novel investigation into the effects of limb morphology of quadrupeds during rapid transient maneuvers such as acceleration and deceleration. Three leg configurations inspired by nature (O-, X-Type and All-Ankle) as well as All-Knee configurations are compared. Extensive large scale Monte Carlo simulations utilizing contact-implicit trajectory optimization methods were employed on 100 randomly generated robots of varying sizes to determine the optimal configuration for the task of rapid transient locomotion. After extensive analysis, the investigation revealed that an X-Type leg configuration outperformed all other configurations. Ultimately, these results will provide insight for the mechanical design of future agile quadruped robots.

Rapid acceleration manoeuvres have been avoided by researchers due to the aperiodicity and complexities of this motion. With the recent improvements in optimal control, this paper presents the first examination of a biped completing a time optimal sprint, starting and ending in rest, to provide insight for parameter choices of a robotic platform. In particular, a realistic linkage morphology is used with the limitation of a pre-specified actuator to choose the nominal leg length and gear ratio. Due to the size of the optimisation problem, a brute force approach is used rather than including these parameters as free variables. The results provided unique motion trajectories for time optimal behaviour with the models reaching near steady state motion and performing manoeuvres that are seen in a biped's biological counterpart. We then show that access to a higher mass-specific force does not improve the rapid acceleration manoeuvres, rather the friction coefficient and keeping the feet near the ground act as the limiting factor given sufficiently powerful actuators. A parabolic relationship emerged for sprint time versus linkage lengths providing valuable insight into the parameters to use for the platform design. To the authors knowledge, no prior research has focused on rapid acceleration and braking manoeuvres of a biped in one optimisation problem, let alone providing insight for the physical bipedal robotic platform.

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.

Animals are able to accelerate rapidly from rest with incredible dexterity but these transient motions are poorly understood. Here we present the first examination of the time optimal behaviour of a quadruped sprinting from rest. We develop a planar multi-body model and employ modern trajectory optimization methods to produce a motion without prescribing periodicity or foot contact order. Our trajectories produce several similarities with racing greyhounds. These results will inspire the design of feedback controllers for future manoeuvrable quadruped robots.

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.

An actuated tail can impart large angular impulse over short time spans, but swinging in a plane results in inevitable tail angle saturation. Cheetahs (Acinonyx jubatus) are observed swinging the tail in a cone during turns [1], and this paper develops a simplified two-degree-of-freedom (pitch and roll) rigid tail model to investigate this motion. Trajectory optimization and experiments on a robotic platform confirm the observed cone motion as a useful solution to roll stabilization. These results are relevant to the understanding of tail motions in biomechanics and bioinspired tailed robots.

Stimulated by recent biomechanics research of the cheetah, a novel tail controller system for rapid acceleration and braking is presented. To understand the targeted behaviour of a cheetah performing a longitudinal manoeuvre and the effects an actuated tail has, a simple mathematical template was developed. Subsequently feedback controllers were designed based on our hypothesis. Finally, the control system was experimentally tested on a reduced order robot model which increased its manoeuvrability considerably.

Inspired by the cheetah, we present a novel tail control system for manoeuvring terrestrial robots at high speed. The mathematic model for a high-speed turn is derived and the model with a tail is shown to be more successful at rapid turns in simulation. We then built a high speed mobile platform with an actuated tail to experimentally validate the control algorithms. Further controller development is performed based on results of the initial simulations. Finally, we show that by rapidly swinging the tail, our system is capable of turning at much higher speeds than a tail-less version.