Yiming Li

Distance functions are crucial in robotics for representing spatial relationships between a robot and its environment. They provide an implicit, continuous, and differentiable representation that integrates seamlessly with control, optimization, and learning. While standard distance fields rely on the Euclidean metric, many robotic tasks inherently involve non-Euclidean structures. To this end, we generalize Euclidean distance fields to more general metric spaces by solving the Riemannian eikonal equation, a first-order partial differential equation whose solution defines a distance field and its associated gradient flow on the manifold, enabling the computation of geodesics and globally length-minimizing paths. We demonstrate that geodesic distance fields —the classical Riemannian distance function represented as a global, continuous, and queryable field—are effective for a broad class of robotic problems where Riemannian geometry naturally arises. To realize this, we present a neural Riemannian eikonal solver (NES) that solves the equation as a mesh-free implicit representation without grid discretization, scaling to high-dimensional robot manipulators. Training leverages a physics-informed neural network (PINN) objective that constrains spatial derivatives via the PDE residual and boundary/metric conditions, so the model is supervised by the governing equation and requires no labeled distances or geodesics. We propose two NES variants, conditioned on boundary data and on spatially varying Riemannian metrics, underscoring the flexibility of the neural parameterization. We validate the effectiveness of our approach through extensive examples, yielding minimal-length geodesics across diverse robot tasks involving Riemannian geometry. Additionally, we validate the method in a dynamics-aware motion-planning task for energy-efficient trajectory generation, with comparisons to baseline approaches. Project website: https://sites.google.com/view/geodf .

Developing autonomous robots capable of learning complex motions from demonstrations remains a fundamental challenge in robotics. On the one hand, movement primitives (MPs) provide a compact and modular representation of continuous trajectories. On the other hand, dynamical systems (DSs) provide control policies that are time-independent. In this letter, we propose a simple and flexible approach called MPDS that gathers the advantages of both representations by transforming MPs into autonomous systems. The key idea is to transform the explicit representation of a trajectory to an implicit shape encoded as a distance field. This conversion from a time-dependent motion to a spatial representation enables the construction of an autonomous dynamical system with modular reactions to perturbation. This approach bridges conventional MPs with distance fields, ensuring smooth and precise motion encoding, while maintaining a continuous spatial representation. We use Bernstein basis functions in the MPs to represent trajectories as concatenated quadratic Bézier curves, which provide an analytical method for computing distance fields. By simply leveraging the analytic gradients of the curve and its distance field, a stable dynamical system can be computed to reproduce the demonstrated trajectories while handling perturbations, without requiring a model of the dynamical system to be estimated. Numerical simulations and real-world robotic experiments validate our method's ability to encode complex motion patterns while ensuring trajectory stability, together with the flexibility of designing the desired reaction to perturbations.

Reasoning about distance is indispensable for establishing or avoiding contact in manipulation tasks. To this end, we present an online approach for learning implicit representations of signed distance using piecewise polynomial basis functions. Starting from an arbitrary prior shape, our method incrementally constructs a continuous and smooth distance representation from incoming surface points, with analytical access to gradient information. The underlying model does not store training data for prediction, and its performance can be balanced through interpretable hyperparameters such as polynomial degree and number of segments. We assess the accuracy of the incrementally learned model on a set of household objects and compare it to neural network and Gaussian process counterparts. The utility of intermediate results and analytical gradients is further demonstrated in a physical experiment.

Human-robot interaction plays an important role in robots serving human production and life. Object handover between humans and robotics is one of the fundamental problems of human-robot interaction. The majority of current work uses parallel-jaw grippers as the end-effector device, which limits the ability of the robot to grab miscellaneous objects from human and manipulate them subsequently. In this paper, we present a framework for human-to-robot dexterous handover using an anthropomorphic hand. The framework takes images captured by two cameras to complete handover scene understanding, grasp configurations prediction, and handover execution. To enable the robot to generalize to diverse delivered objects with miscellaneous shapes and sizes, we propose an anthropomorphic hand grasp network (AHG-Net), an end-to-end network that takes the single-view point clouds of the object as input and predicts the suitable anthropomorphic hand configurations with 5 different grasp taxonomies. To train our model, we build a large-scale dataset with 1M hand grasp annotations from 5K single-view point clouds of 200 objects. We implement a handover system using a UR5 robot arm and HIT-DLR II anthropomorphic robot hand based on our presented framework, which can not only adapt to different human givers but generalize to diverse novel objects with various shapes and sizes. The generalizability, reliability, and robustness of our method are demonstrated on 15 different novel objects with arbitrary handover poses from frontal and lateral positions, a system ablation study, a grasp planner comparison, and a user study on 6 participants delivering 15 objects from two benchmark sets.

Grasping with anthropomorphic robotic hands involves much more hand-object interactions compared to parallel-jaw grippers. Modeling hand-object interactions is essential to the study of multi-finger hand dextrous manipulation. This work presents DVGG, an efficient grasp generation network that takes single-view observation as input and predicts high-quality grasp configurations for unknown objects. In general, our generative model consists of three components: 1) Point cloud completion for the target object based on the partial observation; 2) Diverse sets of grasps generation given the complete point cloud; 3) Iterative grasp pose refinement for physically plausible grasp optimization. To train our model, we build a large-scale grasping dataset that contains about 300 common object models with 1.5 M annotated grasps in simulation. Experiments in simulation show that our model can predict robust grasp poses with a wide variety and high success rate. Real robot platform experiments demonstrate that the model trained on our dataset performs well in the real world. Remarkably, our method achieves a grasp success rate of 70.7% for novel objects in the real robot platform, which is a significant improvement over the baseline methods.