相关论文: Geometry-aware Dynamic Movement Primitives

Generating robot motion for multiple tasks in dynamic environments is challenging, requiring an algorithm to respond reactively while accounting for complex nonlinear relationships between tasks. In this paper, we develop a novel policy…

Despite decades of work in fast reactive planning and control, challenges remain in developing reactive motion policies on non-Euclidean manifolds and enforcing constraints while avoiding undesirable potential function local minima. This…

In this paper, we present new results on the Riemannian geometry of symmetric positive semi-definite (SPSD) matrices. First, based on an existing approximation of the geodesic path, we introduce approximations of the logarithmic and…

Robots operating in human-centric environments must be both robust to disturbances and provably safe from collisions. Achieving these properties simultaneously and efficiently remains a central challenge. While Dynamic Movement Primitives…

The effectiveness of Symmetric Positive Definite (SPD) manifold features has been proven in various computer vision tasks. However, due to the non-Euclidean geometry of these features, existing Euclidean machineries cannot be directly used.…

Pre-defined manipulation primitives are widely used for cloth manipulation. However, cloth properties such as its stiffness or density can highly impact the performance of these primitives. Although existing solutions have tackled the…

We develop a novel policy synthesis algorithm, RMPflow, based on geometrically consistent transformations of Riemannian Motion Policies (RMPs). RMPs are a class of reactive motion policies designed to parameterize non-Euclidean behaviors as…

Movement Primitives (MPs) are a well-known concept to represent and generate modular trajectories. MPs can be broadly categorized into two types: (a) dynamics-based approaches that generate smooth trajectories from any initial state, e. g.,…

Manifolds occur naturally as configuration spaces of robotic systems. They provide global descriptions of local coordinate systems that are common tools in expressing positions of robots. The purpose of this survey is threefold. Firstly, we…

We aim to develop an efficient programming method for equipping service robots with the skill of performing sign language motions. This paper addresses the problem of transferring complex dual-arm sign language motions characterized by the…

Body posture influences human and robots performance in manipulation tasks, as appropriate poses facilitate motion or force exertion along different axes. In robotics, manipulability ellipsoids arise as a powerful descriptor to analyze,…

Probabilistic representations of movement primitives open important new possibilities for machine learning in robotics. These representations are able to capture the variability of the demonstrations from a teacher as a probability…

In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive…

Riemannian submanifold optimization with momentum is computationally challenging because, to ensure that the iterates remain on the submanifold, we often need to solve difficult differential equations. Here, we simplify such difficulties…

Solving the inverse kinematics problem is a fundamental challenge in motion planning, control, and calibration for articulated robots. Kinematic models for these robots are typically parametrized by joint angles, generating a complicated…

Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly…

Differential geometric approaches to the analysis and processing of data in the form of symmetric positive definite (SPD) matrices have had notable successful applications to numerous fields including computer vision, medical imaging, and…

Modeling and control of high-dimensional, nonlinear robotic systems remains a challenging task. While various model- and learning-based approaches have been proposed to address these challenges, they broadly lack generalizability to…

Data-driven models of robot motion constructed using principles from Geometric Mechanics have been shown to produce useful predictions of robot motion for a variety of robots. For robots with a useful number of DoF, these geometric…

Robotic manipulators operating in dynamic and uncertain environments require efficient motion planning to navigate obstacles while maintaining smooth trajectories. Velocity Potential Field (VPF) planners offer real-time adaptability but…