CAJun: Continuous Adaptive Jumping using a Learned Centroidal Controller

We present CAJun, a novel hierarchical learning and control framework that enables legged robots to jump continuously with adaptive jumping distances. CAJun consists of a high-level centroidal policy and a low-level leg controller. In particular, we use reinforcement learning (RL) to train the centroidal policy, which specifies the gait timing, base velocity, and swing foot position for the leg controller. The leg controller optimizes motor commands for the swing and stance legs according to the gait timing to track the swing foot target and base velocity commands using optimal control. Additionally, we reformulate the stance leg optimizer in the leg controller to speed up policy training by an order of magnitude. Our system combines the versatility of learning with the robustness of optimal control. By combining RL with optimal control methods, our system achieves the versatility of learning while enjoys the robustness from control methods, making it easily transferable to real robots. We show that after 20 minutes of training on a single GPU, CAJun can achieve continuous, long jumps with adaptive distances on a Go1 robot with small sim-to-real gaps. Moreover, the robot can jump across gaps with a maximum width of 70cm, which is over 40% wider than existing methods.Comment: Please visit https://yxyang.github.io/cajun/ for additional result

Towards Agility: A Momentum Aware Trajectory Optimisation Framework using Full-Centroidal Dynamics & Implicit Inverse Kinematics

Online planning and execution of acrobatic maneuvers pose significant challenges in legged locomotion. Their underlying combinatorial nature, along with the current hardware's limitations constitute the main obstacles in unlocking the true potential of legged-robots. This letter tries to expose the intricacies of these optimal control problems in a tangible way, directly applicable to the creation of more efficient online trajectory optimisation frameworks. By analysing the fundamental principles that shape the behaviour of the system, the dynamics themselves can be exploited to surpass its hardware limitations. More specifically, a trajectory optimisation formulation is proposed that exploits the system's high-order nonlinearities, such as the nonholonomy of the angular momentum, and phase-space symmetries in order to produce feasible high-acceleration maneuvers. By leveraging the full-centroidal dynamics of the quadruped ANYmal C and directly optimising its footholds and contact forces, the framework is capable of producing efficient motion plans with low computational overhead. The feasibility of the produced trajectories is ensured by taking into account the configuration-dependent inertial properties of the robot during the planning process, while its robustness is increased by supplying the full analytic derivatives & hessians to the solver. Finally, a significant portion of the discussion is centred around the deployment of the proposed framework on the ANYmal C platform, while its true capabilities are demonstrated through real-world experiments, with the successful execution of high-acceleration motion scenarios like the squat-jump

Efficient Motion Planning for Deformable Objects with High Degrees of Freedom

Many robotics and graphics applications need to be able to plan motions by interacting with complex environmental objects, including solids, sands, plants, and fluids. A key aspect of these deformable objects is that they have high-DOF, which implies that they can move or change shapes in many independent ways subject to physics-based constraints. In these applications, users also impose high-level goals on the movements of high-DOF objects, and planning algorithms need to model their motions and determine the optimal control actions to satisfy the high-level goals. In this thesis, we propose several planning algorithms for high-DOF objects. Our algorithms can improve the scalability considerably and can plan motions for different types of objects, including elastically deformable objects, free-surface flows, and Eulerian fluids. We show that the salient deformations of elastically deformable objects lie in a low-dimensional nonlinear space, i.e., the RS space. By embedding the configuration space in the RS subspace, our optimization-based motion planning algorithm can achieve over two orders of magnitude speedup over prior optimization-based formulations. For free surface flows such as liquids, we utilize features of the planning problems and machine learning techniques to identify low-dimensional latent spaces to accelerate the motion planning computation. For Eulerian fluids without free surfaces, we present a scalable planning algorithm based on novel numerical techniques. We show that the numerical discretization scheme exhibits strong regularity, which allows us to accelerate optimization-based motion planning algorithms using a hierarchical data structure and we can achieve 3-10 times speedup over gradient-based optimization techniques. Finally, for high-DOF objects with many frictional contacts with the environment, we present a contact dynamic model that can handle contacts without expensive combinatorial optimization. We illustrate the benefits of our high-DOF planning algorithms for three applications. First, we can plan contact-rich motion trajectories for general elastically deformable robots. Second, we can achieve real-time performance in terms of planning the motion of a robot arm to transfer the liquids between containers. Finally, our method enables a more intuitive user interface. We allow animation editors to modify animations using an offline motion planner to generate controlled fluid animations.Doctor of Philosoph

Optimization-Based Control for Dynamic Legged Robots

In a world designed for legs, quadrupeds, bipeds, and humanoids have the opportunity to impact emerging robotics applications from logistics, to agriculture, to home assistance. The goal of this survey is to cover the recent progress toward these applications that has been driven by model-based optimization for the real-time generation and control of movement. The majority of the research community has converged on the idea of generating locomotion control laws by solving an optimal control problem (OCP) in either a model-based or data-driven manner. However, solving the most general of these problems online remains intractable due to complexities from intermittent unidirectional contacts with the environment, and from the many degrees of freedom of legged robots. This survey covers methods that have been pursued to make these OCPs computationally tractable, with specific focus on how environmental contacts are treated, how the model can be simplified, and how these choices affect the numerical solution methods employed. The survey focuses on model-based optimization, covering its recent use in a stand alone fashion, and suggesting avenues for combination with learning-based formulations to further accelerate progress in this growing field.Comment: submitted for initial review; comments welcom

A contact-implicit direct trajectory optimization scheme for the study of legged maneuverability

For legged robots to move safely in unpredictable environments, they need to be manoeuvrable, but transient motions such as acceleration, deceleration and turning have been the subject of little research compared to constant-speed gait. They are difficult to study for two reasons: firstly, the way they are executed is highly sensitive to factors such as morphology and traction, and secondly, they can potentially be dangerous, especially when executed rapidly, or from high speeds. These challenges make it an ideal topic for study by simulation, as this allows all variables to be precisely controlled, and puts no human, animal or robotic subjects at risk. Trajectory optimization is a promising method for simulating these manoeuvres, because it allows complete motion trajectories to be generated when neither the input actuation nor the output motion is known. Furthermore, it produces solutions that optimize a given objective, such as minimizing the distance required to stop, or the effort exerted by the actuators throughout the motion. It has consequently become a popular technique for high-level motion planning in robotics, and for studying locomotion in biomechanics. In this dissertation, we present a novel approach to studying motion with trajectory optimization, by viewing it more as “trajectory generation” – a means of generating large quantities of synthetic data that can illuminate the differences between successful and unsuccessful motion strategies when studied in aggregate. One distinctive feature of this approach is the focus on whole-body models, which capture the specific morphology of the subject, rather than the highly-simplified “template” models that are typically used. Another is the use of “contact-implicit” methods, which allow an appropriate footfall sequence to be discovered, rather than requiring that it be defined upfront. Although contact-implicit methods are not novel, they are not widely-used, as they are computationally demanding, and unnecessary when studying comparatively-predictable constant speed locomotion. The second section of this dissertation describes innovations in the formulation of these trajectory optimization problems as nonlinear programming problems (NLPs). This “direct” approach allows these problems to be solved by general-purpose, open-source algorithms, making it accessible to scientists without the specialized applied mathematics knowledge required to solve NLPs. The design of the NLP has a significant impact on the accuracy of the result, the quality of the solution (with respect to the final value of the objective function), and the time required to solve the proble

Imaging neural activity in the ventral nerve cord of behaving adult Drosophila

To understand neural circuits that control limbs, one must measure their activity during behavior. Until now this goal has been challenging, because limb premotor and motor circuits have been largely inaccessible for large-scale recordings in intact, moving animals-a constraint that is true for both vertebrate and invertebrate models. Here, we introduce a method for 2-photon functional imaging from the ventral nerve cord (VNC) of behaving adult Drosophila melanogaster. We use this method to reveal patterns of activity across nerve cord populations during grooming and walking and to uncover the functional encoding of moonwalker ascending neurons (MANs), moonwalker descending neurons (MDNs), and a previously uncharacterized class of locomotion-associated A1 descending neurons. Finally, we develop a genetic reagent to destroy the indirect flight muscles and to facilitate experimental access to the VNC. Taken together, these approaches enable the direct investigation of circuits associated with complex limb movements

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described