Autonomous robots typically need to construct representations of their surroundings and adapt their motions to the geometry of their environment. Here, we tackle the problem of constructing a policy model for collision-free motion generation, consistent with the environment, from a single input RGB image. Extracting 3D structures from a single image often involves monocular depth estimation. Developments in depth estimation have given rise to large pre-trained models such as \emph{DepthAnything}. However, using outputs of these models for downstream motion generation is challenging due to frustum-shaped errors that arise. Instead, we propose a framework known as Video-Generation Environment Representation (VGER), which leverages the advances of large-scale video generation models to generate a moving camera video conditioned on the input image. Frames of this video, which form a multiview dataset, are then input into a pre-trained 3D foundation model to produce a dense point cloud. We then introduce a multi-scale noise approach to train an implicit representation of the environment structure and build a motion generation model that complies with the geometry of the representation. We extensively evaluate VGER over a diverse set of indoor and outdoor environments. We demonstrate its ability to produce smooth motions that account for the captured geometry of a scene, all from a single RGB input image.

Robotic manipulator applications often require efficient online motion planning. When completing multiple tasks, sequence order and choice of goal configuration can have a drastic impact on planning performance. This is well known as the robot task sequencing problem (RTSP). Existing general-purpose RTSP algorithms are susceptible to producing poor-quality solutions or failing entirely when available computation time is restricted. We propose a new multiquery task sequencing method designed to operate in semistructured environments with a combination of static and nonstatic obstacles. Our method intentionally trades off workspace generality for planning efficiency. Given a user-defined task space with static obstacles, we compute a subspace decomposition. The key idea is to establish approximate isometries known as$\epsilon$-Gromov-Hausdorff approximations that identify points that are close to one another in both task and configuration space. Importantly, we prove bounded suboptimality guarantees on the lengths of paths within these subspaces. These bounding relations further imply that paths within the same subspace can be smoothly concatenated, which we show is useful for determining efficient task sequences. We evaluate our method with several kinematic configurations in a complex simulated environment, achieving up to 3× faster motion planning and 5× lower maximum trajectory jerk compared to baselines.

Pedestrian trajectory prediction plays an important role in autonomous driving systems and robotics. Recent work utilizing prominent deep learning models for pedestrian motion prediction makes limited a priori assumptions about human movements, resulting in a lack of explainability and explicit constraints enforced on predicted trajectories. We present a dynamics-based deep learning framework with a novel asymptotically stable dynamical system integrated into a Transformer-based model. We use an asymptotically stable dynamical system to model human goal-targeted motion by enforcing the human walking trajectory, which converges to a predicted goal position, and to provide the Transformer model with prior knowledge and explainability. Our framework features the Transformer model that works with a goal estimator and dynamical system to learn features from pedestrian motion history. The results show that our framework outperforms prominent models using five benchmark human motion datasets.

Learning from Demonstration (LfD) enables robots to acquire new skills by imitating expert demonstrations, allowing users to communicate their instructions intuitively. Recent progress in LfD often relies on kinesthetic teaching or teleoperation as the medium for users to specify the demonstrations. Kinesthetic teaching requires physical handling of the robot, while teleoperation demands proficiency with additional hardware. This paper introduces an alternative paradigm for LfD called Diagrammatic Teaching. Diagrammatic Teaching aims to teach robots novel skills by prompting the user to sketch out demonstration trajectories on 2D images of the scene, these are then synthesised as a generative model of motion trajectories in 3D task space. Additionally, we present the Ray-tracing Probabilistic Trajectory Learning (RPTL) framework for Diagrammatic Teaching. RPTL extracts time-varying probability densities from the 2D sketches, then applies ray-tracing to find corresponding regions in 3D Cartesian space, and fits a probabilistic model of motion trajectories to these regions. New motion trajectories, which mimic those sketched by the user, can then be generated from the probabilistic model. We empirically validate our framework both in simulation and on real robots, which include a fixed-base manipulator and a quadruped-mounted manipulator.

This paper introduces Spatial Diagrammatic Instructions (SDIs), an approach for human operators to specify objectives and constraints that are related to spatial regions in the working environment. Human operators are enabled to sketch out regions directly on camera images that correspond to the objectives and constraints. These sketches are projected to 3D spatial coordinates, and continuous Spatial Instruction Maps (SIMs) are learned upon them. These maps can then be integrated into optimization problems for tasks of robots. In particular, we demonstrate how Spatial Diagrammatic Instructions can be applied to solve the Base Placement Problem of mobile manipulators, which concerns the best place to put the manipulator to facilitate a certain task. Human operators can specify, via sketch, spatial regions of interest for a manipulation task and permissible regions for the mobile manipulator to be at. Then, an optimization problem that maximizes the manipulator’s reachability, or coverage, over the designated regions of interest while remaining in the permissible regions is solved. We provide extensive empirical evaluations, and show that our formulation of Spatial Instruction Maps provides accurate representations of user-specified diagrammatic instructions. Furthermore, we demonstrate that our diagrammatic approach to the Mobile Base Placement Problem enables higher quality solutions and faster runtime.

We integrate neural networks into kinodynamic motion planning and present the Learning for KinoDynamic Tree Expansion (L4KDE) method. Tree-based planning approaches, such as rapidly exploring random tree (RRT), are the dominant approach to finding globally optimal plans in continuous state-space motion planning. Central to these approaches is tree expansion, the procedure in which new nodes are added to an ever-expanding tree. We study the kinodynamic variants of tree-based planning, where we have known system dynamics and kinematic constraints. In the interest of quickly selecting nodes to connect newly sampled coordinates, existing methods typically cannot optimise the finding of nodes that have a low cost to transition to sampled coordinates. Instead, they use metrics like Euclidean distance between coordinates as a heuristic for selecting candidate nodes to connect to the search tree. We propose L4KDE to address this issue. L4KDE uses a neural network to predict transition costs between queried states, which can be efficiently computed in batch, providing much higher quality estimates of transition cost compared to commonly used heuristics while maintaining almost-surely asymptotic optimality guarantee. We empirically demonstrate the significant performance improvement provided by L4KDE on a variety of challenging system dynamics,with the ability to generalise across different instances of the same model class and in conjunction with a suite of modern tree-based motion planners.

The ability to construct concise scene representations from sensor input is central to the field of robotics. This paper addresses the problem of robustly creating a 3D representation of a tabletop scene from a segmented RGBD image. These representations are then critical for a range of downstream manipulation tasks. Many previous attempts to tackle this problem do not capture accurate uncertainty, which is required to subsequently produce safe motion plans. In this paper, we cast the representation of 3D tabletop scenes as a multi-class classification problem. To tackle this, we introduce V-PRISM, a framework and method for robustly creating probabilistic 3D segmentation maps of tabletop scenes. Our maps contain both occupancy estimates, segmentation information, and principled uncertainty measures. We evaluate the robustness of our method in (1) procedurally generated scenes using open-source object datasets, and (2) real-world tabletop data collected from a depth camera. Our experiments show that our approach outperforms alternative continuous reconstruction approaches that do not explicitly reason about objects in a multi-class formulation.

Humans have the remarkable ability to construct consistent mental models of an environment, even under limited or varying levels of illumination. We wish to endow robots with this same capability. In this paper, we tackle the challenge of constructing a photorealistic scene representation under poorly illuminated conditions and with a moving light source. We approach the task of modeling illumination as a learning problem, and utilize the developed illumination model to aid in scene reconstruction. We introduce an innovative framework that uses a data-driven approach, Neural Light Simulators (NeLiS), to model and calibrate the camera-light system. Furthermore, we present DarkGS, a method that applies NeLiS to create a relightable 3D Gaussian scene model capable of real-time, photorealistic rendering from novel viewpoints. We show the applicability and robustness of our proposed simulator and system in a variety of real-world environments. Code released at https://tyz1030.github.io/proj/darkgs.html

Motion generation seeks to produce safe and feasible robot motion from start to goal. Various tools at different levels of granularity have been developed. On one extreme, sampling-based motion planners focus on completeness - a solution, if it exists, would eventually be found. However, produced paths are often of low quality, and contain superfluous motion. On the other, reactive methods optimise the immediate cost to obtain the next controls, producing smooth and legible motion that can quickly adapt to perturbations, uncertainties, and changes in the environment. However, reactive methods are highly local, and often produce motion that become trapped in non-convex regions of the environment. This paper contributes, Geometric Fabric Command Sequences, a method that lies in the middle ground. It can produce globally optimal motion that is smooth and intuitive, while being also reactive. We model motion via a reactive Geometric Fabric policy that ingests a sequence of attractor states, or commands, and then apply global optimisation over the space of commands. We postulate that solutions for different problems and scenes are highly transferable when conditioned on environmental features. Therefore, an implicit generative model is trained on solutions from optimisation and environment features in a self-supervised manner. That is, faced with multiple motion generation problems, the learning and optimisation are contained within the same loop: the optimisation generates labels for learning, while the learning improves the optimisation for the next problem, which in turn provides higher quality labels. We empirically validate our method in both simulation and on a real-world 6-DOF JACO arm.

Advances in differentiable numerical integrators have enabled the use of gradient descent techniques to learn ordinary differential equations (ODEs), where a flexible function approximator (often a neural network) is used to estimate the system dynamics, given as a time derivative. However, these integrators can be unsatisfactorily slow and unstable when learning systems of ODEs from long sequences. We propose to learn an ODE of interest from data by viewing its dynamics as a vector field related to another base vector field via a diffeomorphism (i.e., a differentiable bijection), represented by an invertible neural network (INN). By learning both the INN and the dynamics of the base ODE, we provide an avenue to offload some of the complexity in modelling the dynamics directly on to the INN. Consequently, by restricting the base ODE to be amenable to integration, we can speed up and improve the robustness of integrating trajectories from the learned system. We demonstrate the efficacy of our method in training and evaluating benchmark ODE systems, as well as within continuous-depth neural networks models. We show that our approach attains speed-ups of up to two orders of magnitude when integrating learned ODEs.

Critical for the coexistence of humans and robots in dynamic environments is the capability for agents to understand each other’s actions, and anticipate their movements. This paper presents Stochastic Process Anticipatory Navigation (SPAN), a framework that enables nonholonomic robots to navigate in environments with crowds, while anticipating and accounting for the motion patterns of pedestrians. To this end, we learn a predictive model to predict continuous-time stochastic processes to model future movement of pedestrians. Anticipated pedestrian positions are used to conduct chance constrained collision-checking, and are incorporated into a time-to-collision control problem. An occupancy map is also integrated to allow for probabilistic collision-checking with static obstacles. We demonstrate the capability of SPAN in crowded simulation environments, as well as with a real-world pedestrian dataset.

Being able to safely operate for extended periods of time in dynamic environments is a critical capability for autonomous systems. This generally involves the prediction and understanding of motion patterns of dynamic entities, such as vehicles and people, in the surroundings. Many motion prediction methods in the literature implicitly account for environmental factors by learning on observed motion in a fixed environment, and are designed to make predictions in the same environment. In this paper, we address the problem of generating likely motion trajectories for novel environments, represented as occupancy grid maps, where motion has not been observed. We introduce the Occupancy-Conditional Trajectory Network (OTNet) framework, capable of transferring the previously observed motion patterns in known environments to new environments. OTNet provides a functional representation for motion trajectories and utilises neural networks to learn occupancy-conditional distributions over the function parameters. We empirically demonstrate our method’s ability to generate complex multi-modal trajectory patterns in both simulated and real-world environments.

This work addresses the problem of predicting the motion trajectories of dynamic objects in the environment. Recent advances in predicting motion patterns often rely on machine learning techniques to extrapolate motion patterns from observed trajectories, with no mechanism to directly incorporate known rules. We propose a novel framework, which combines probabilistic learning and constrained trajectory optimisation. The learning component of our framework provides a distribution over future motion trajectories conditioned on observed past coordinates. This distribution is then used as a prior to a constrained optimisation problem which enforces chance constraints on the trajectory distribution. This results in constraint-compliant trajectory distributions which closely resemble the prior. In particular, we focus our investigation on collision constraints, such that extrapolated future trajectory distributions conform to the environment structure. We empirically demonstrate on real-world and simulated datasets the ability of our framework to learn complex probabilistic motion trajectories for motion data, while directly enforcing constraints to improve generalisability, producing more robust and higher quality trajectory distributions.

Mapping the occupancy of an environment is central for robot autonomy. Traditional occupancy grid maps discretise the environment into independent cells, neglecting important spatial correlations, and are unable to capture the continuous nature of the real world. With these drawbacks of grid maps in mind, Hilbert Maps (HM) and more recently Bayesian Hilbert Maps (BHMs), were introduced as a continuous representation of the environment. In this paper we propose a method to merge Bayesian Hilbert Maps built by a team of robots in a decentralised manner. The training of BHMs requires the inversion of a large covariance matrix, incurring cubic complexity. We introduce an approximation, Fast Bayesian Hilbert Maps (Fast-BHM), which reduces the time complexity to below quadratic. Such speed-ups allow the building and merging of Bayesian Hilbert Map models to be practical, opening the door for multi-robot Hilbert Map systems which can be much faster and more robust than an individual robot. By merging several individual Fast-BHMs in a decentralised manner we obtain a unified model of the environment which is itself a Fast-BHM. We conduct experiments to show that global Fast-BHM models do not deteriorate after repeated merging and training. We then empirically demonstrate, due to its the compact representation, fused Fast-BHMs outperform fusion methods involving discretising continuous representations, when the amount of information communicated is limited.