Robotic locomotion is often approached with the goal of maximizing robustness and reactivity by increasing motion control frequency. We challenge this intuitive notion by demonstrating robust and dynamic locomotion with a learned motion controller executing at as low as 8 Hz on a real ANYmal C quadruped. The robot is able to robustly and repeatably achieve a high heading velocity of 1.5 ms-1, traverse uneven terrain, and resist unexpected external perturbations. We further present a comparative analysis of deep reinforcement learning (RL) based motion control policies trained and executed at frequencies ranging from 5 Hz to 200 Hz. We show that low-frequency policies are less sensitive to actuation latencies and variations in system dynamics. This is to the extent that a successful sim- to-real transfer can be performed even without any dynamics randomization or actuation modeling. We support this claim through a set of rigorous empirical evaluations. Moreover, to assist reproducibility, we provide the training and deployment code along with an extended analysis at https://ori-drs.github.io/lfmc/.

Quadruped locomotion is rapidly maturing to a degree where robots are able to realize highly dynamic maneuvers. However, current planners are unable to vary key gait parameters of the in-swing feetmidair. In this article, we address this limitation and show that it is pivotal in increasing controller robustness by learning a latent space capturing the key stance phases constituting a particular gait. This is achieved via a generative model trained on a single trot style, which encourages disentanglement such that application of a drive signal to a single dimension of the latent state induces holistic plans synthesizing a continuous variety of trot styles. We demonstrate that specific properties of the drive signal map directly to gait parameters, such as cadence, footstep height, and full-stance duration. Due to the nature of our approach, these synthesized gaits are continuously variable online during robot operation. The use of a generative model facilitates the detection and mitigation of disturbances to provide a versatile and robust planning framework. We evaluate our approach on two versions of the real ANYmal quadruped robots and demonstrate that our method achieves a continuous blend of dynamic trot styles while being robust and reactive to external perturbations.

Quadruped locomotion is rapidly maturing to a degree where robots now routinely traverse a variety of unstructured terrains. However, while gaits can be varied typically by selecting from a range of pre-computed styles, current planners are unable to vary key gait parameters continuously while the robot is in motion. The synthesis, on-the-fly, of gaits with unexpected operational characteristics or even the blending of dynamic manoeuvres lies beyond the capabilities of the current state-of-the-art. In this work we address this limitation by learning a latent space capturing the key stance phases of a particular gait, via a generative model trained on a single trot style. This encourages disentanglement such that application of a drive signal to a single dimension of the latent state induces holistic plans synthesising a continuous variety of trot styles. In fact properties of this drive signal map directly to gait parameters such as cadence, footstep height and full stance duration. The use of a generative model facilitates the detection and mitigation of disturbances to provide a versatile and robust planning framework. We evaluate our approach on a real ANYmal quadruped robot and demonstrate that our method achieves a continuous blend of dynamic trot styles whilst being robust and reactive to external perturbations.

We present a unified model-based and data-driven approach for quadrupedal planning and control to achieve dynamic locomotion over uneven terrain. We utilize on-board proprioceptive and exteroceptive feedback to map sensory information and desired base velocity commands into footstep plans using a reinforcement learning (RL) policy. This RL policy is trained in simulation over a wide range of procedurally generated terrains. When run online, the system tracks the generated footstep plans using a model-based motion controller. We evaluate the robustness of our method over a wide variety of complex terrains. It exhibits behaviors that prioritize stability over aggressive locomotion. Additionally, we introduce two ancillary RL policies for corrective whole-body motion tracking and recovery control. These policies account for changes in physical parameters and external perturbations. We train and evaluate our framework on a complex quadrupedal system, ANYmal version B, and demonstrate transferability to a larger and heavier robot, ANYmal C, without requiring retraining.

We present a control architecture for real-time adaptation and tracking of trajectories generated using a terrain-aware trajectory optimization solver. This approach enables us to circumvent the computationally exhaustive task of online trajectory optimization, and further introduces a control solution robust to systems modeled with approximated dynamics. We train a policy using deep reinforcement learning (RL) to introduce additive deviations to a reference trajectory in order to generate a feedback-based trajectory tracking system for a quadrupedal robot. We train this policy across a multitude of simulated terrains and ensure its generality by introducing training methods that avoid overfitting and convergence towards local optima. Additionally, in order to capture terrain information, we include a latent representation of the height maps in the observation space of the RL environment as a form of exteroceptive feedback. We test the performance of our trained policy by tracking the corrected set points using a model-based whole-body controller and compare it with the tracking behavior obtained without the corrective feedback in several simulation environments, and show that introducing the corrective feedback results in increase of the success rate from 72.7% to 92.4% for tracking precomputed dynamic long horizon trajectories on flat terrain and from 47.5% to 80.3% on a complex modular uneven terrain. We also show successful transfer of our training approach to the real physical system and further present cogent arguments in support of our framework.

The efficient evaluation the dynamic stability of legged robots on non-coplanar terrains is important when developing motion planning and control policies. The inference time of this measure has a strong influence on how fast a robot can react to unexpected events, plan its future footsteps or its body trajectory. Existing approaches suitable for real-time decision making are either limited to flat ground or to quasi-static locomotion. Furthermore, joint-space feasibility constraints are usually not considered in receding-horizon planning as their high dimensionality prohibits this. In this paper we propose the usage of a stability criterion for dynamic locomotion on rough terrain based on the Feasible Region (FR) and the Instantaneous Capture Point (ICP) and we leverage a Neural Network (NN) to quickly estimate it. We show that our network achieves satisfactory accuracy with respect to its analytical counterpart with a speed up of three orders-of-magnitude. It also enables the evaluation of the stability margin's gradient. We demonstrate this learned stability margin in two diverse applications - Reinforcement Learning (RL) and nonlinear Trajectory Optimization (TO) for legged robots. We demonstrate on a full-sized quadruped robot that the network enables the computation of physically-realizable Center of Mass (CoM) trajectories and foothold locations satisfying friction constraints and joint-torque limits in a receding-horizon fashion and on non-coplanar terrains.

Traditional approaches to quadruped control frequently employ simplified, hand-derived models. This significantly reduces the capability of the robot since its effective kinematic range is curtailed. In addition, kinodynamic constraints are often non-differentiable and difficult to implement in an optimisation approach. In this work, these challenges are addressed by framing quadruped control as optimisation in a structured latent space. A deep generative model captures a statistical representation of feasible joint configurations, whilst complex dynamic and terminal constraints are expressed via high-level, semantic indicators and represented by learned classifiers operating upon the latent space. As a consequence, complex constraints are rendered differentiable and evaluated an order of magnitude faster than analytical approaches. We validate the feasibility of locomotion trajectories optimised using our approach both in simulation and on a real-world ANY-mal quadruped. Our results demonstrate that this approach is capable of generating smooth and realisable trajectories. To the best of our knowledge, this is the first time latent space control has been successfully applied to a complex, real robot platform.