VAE-Loco: Versatile Quadruped Locomotion by Learning a Disentangled Gait Representation

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 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 synthesising 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 synthesised gaits are continuously variable online during robot operation and robustly capture a richness of movement significantly exceeding the relatively narrow behaviour seen during training. In addition, 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 whilst being robust and reactive to external perturbations.

Next Steps: Learning a Disentangled Gait Representation for Versatile Quadruped Locomotion

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 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 synthesising a continuous variety of trot styles. We demonstrate that specific properties of the drive signal map directly to gait parameters such as cadence, foot step height and full stance duration. Due to the nature of our approach these synthesised gaits are continuously variable online during robot operation and robustly capture a richness of movement significantly exceeding the relatively narrow behaviour seen during training. In addition, 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.

Universal Approximation of Functions on Sets

Modelling functions of sets, or equivalently, permutation-invariant functions, is a long-standing challenge in machine learning. Deep Sets is a popular method which is known to be a universal approximator for continuous set functions. We provide a theoretical analysis of Deep Sets which shows that this universal approximation property is only guaranteed if the model's latent space is sufficiently high-dimensional. If the latent space is even one dimension lower than necessary, there exist piecewise-affine functions for which Deep Sets performs no better than a na\"ive constant baseline, as judged by worst-case error. Deep Sets may be viewed as the most efficient incarnation of the Janossy pooling paradigm. We identify this paradigm as encompassing most currently popular set-learning methods. Based on this connection, we discuss the implications of our results for set learning more broadly, and identify some open questions on the universality of Janossy pooling in general.

APEX: Unsupervised, Object-Centric Scene Segmentation and Tracking for Robot Manipulation

Recent advances in unsupervised learning for object detection, segmentation, and tracking hold significant promise for applications in robotics. A common approach is to frame these tasks as inference in probabilistic latent-variable models. In this paper, however, we show that the current state-of-the-art struggles with visually complex scenes such as typically encountered in robot manipulation tasks. We propose APEX, a new latent-variable model which is able to segment and track objects in more realistic scenes featuring objects that vary widely in size and texture, including the robot arm itself. This is achieved by a principled mask normalisation algorithm and a high-resolution scene encoder. To evaluate our approach, we present results on the real-world Sketchy dataset. This dataset, however, does not contain ground truth masks and object IDs for a quantitative evaluation. We thus introduce the Panda Pushing Dataset (P2D) which shows a Panda arm interacting with objects on a table in simulation and which includes ground-truth segmentation masks and object IDs for tracking. In both cases, APEX comprehensively outperforms the current state-of-the-art in unsupervised object segmentation and tracking. We demonstrate the efficacy of our segmentations for robot skill execution on an object arrangement task, where we also achieve the best or comparable performance among all the baselines.

GENESIS-V2: Inferring Unordered Object Representations without Iterative Refinement

Advances in object-centric generative models (OCGMs) have culminated in the development of a broad range of methods for unsupervised object segmentation and interpretable object-centric scene generation. These methods, however, are limited to simulated and real-world datasets with limited visual complexity. Moreover, object representations are often inferred using RNNs which do not scale well to large images or iterative refinement which avoids imposing an unnatural ordering on objects in an image but requires the a priori initialisation of a fixed number of object representations. In contrast to established paradigms, this work proposes an embedding-based approach in which embeddings of pixels are clustered in a differentiable fashion using a stochastic, non-parametric stick-breaking process. Similar to iterative refinement, this clustering procedure also leads to randomly ordered object representations, but without the need of initialising a fixed number of clusters a priori. This is used to develop a new model, GENESIS-V2, which can infer a variable number of object representations without using RNNs or iterative refinement. We show that GENESIS-V2 outperforms previous methods for unsupervised image segmentation and object-centric scene generation on established synthetic datasets as well as more complex real-world datasets.

Reconstruction Bottlenecks in Object-Centric Generative Models

A range of methods with suitable inductive biases exist to learn interpretable object-centric representations of images without supervision. However, these are largely restricted to visually simple images; robust object discovery in real-world sensory datasets remains elusive. To increase the understanding of such inductive biases, we empirically investigate the role of "reconstruction bottlenecks" for scene decomposition in GENESIS, a recent VAE-based model. We show such bottlenecks determine reconstruction and segmentation quality and critically influence model behaviour.

First Steps: Latent-Space Control with Semantic Constraints for Quadruped Locomotion

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 ANYmal 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.

RELATE: Physically Plausible Multi-Object Scene Synthesis Using Structured Latent Spaces

We present RELATE, a model that learns to generate physically plausible scenes and videos of multiple interacting objects. Similar to other generative approaches, RELATE is trained end-to-end on raw, unlabeled data. RELATE combines an object-centric GAN formulation with a model that explicitly accounts for correlations between individual objects. This allows the model to generate realistic scenes and videos from a physically-interpretable parameterization. Furthermore, we show that modeling the object correlation is necessary to learn to disentangle object positions and identity. We find that RELATE is also amenable to physically realistic scene editing and that it significantly outperforms prior art in object-centric scene generation in both synthetic (CLEVR, ShapeStacks) and real-world data (street traffic scenes). In addition, in contrast to state-of-the-art methods in object-centric generative modeling, RELATE also extends naturally to dynamic scenes and generates videos of high visual fidelity

GENESIS: Generative Scene Inference and Sampling with Object-Centric Latent Representations

Generative models are emerging as promising tools in robotics and reinforcement learning. Yet, even though tasks in these domains typically involve distinct objects, most state-of-the-art methods do not explicitly capture the compositional nature of visual scenes. Two exceptions, MONet and IODINE, decompose scenes into objects in an unsupervised fashion via a set of latent variables. Their underlying generative processes, however, do not account for component interactions. Hence, neither of them allows for principled sampling of coherent scenes. Here we present GENESIS, the first object-centric generative model of visual scenes capable of both decomposing and generating complete scenes by explicitly capturing relationships between scene components. GENESIS parameterises a spatial GMM over pixels which is encoded by component-wise latent variables that are inferred sequentially or sampled from an autoregressive prior. We train GENESIS on two publicly available datasets and probe the information in the latent representations through a set of classification tasks, outperforming several baselines.

On the Limitations of Representing Functions on Sets

Recent work on the representation of functions on sets has considered the use of summation in a latent space to enforce permutation invariance. In particular, it has been conjectured that the dimension of this latent space may remain fixed as the cardinality of the sets under consideration increases. However, we demonstrate that the analysis leading to this conjecture requires mappings which are highly discontinuous and argue that this is only of limited practical use. Motivated by this observation, we prove that an implementation of this model via continuous mappings (as provided by e.g. neural networks or Gaussian processes) actually imposes a constraint on the dimensionality of the latent space. Practical universal function representation for set inputs can only be achieved with a latent dimension at least the size of the maximum number of input elements.