A sampling-based planner approximates Riemannian geodesic distances via midpoints with third-order accuracy and uses retractions plus natural gradients for local planning, producing lower-cost trajectories than Euclidean baselines on robotic arms and SE(2) systems.
Riemannian Motion Policies
8 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We introduce the Riemannian Motion Policy (RMP), a new mathematical object for modular motion generation. An RMP is a second-order dynamical system (acceleration field or motion policy) coupled with a corresponding Riemannian metric. The motion policy maps positions and velocities to accelerations, while the metric captures the directions in the space important to the policy. We show that RMPs provide a straightforward and convenient method for combining multiple motion policies and transforming such policies from one space (such as the task space) to another (such as the configuration space) in geometrically consistent ways. The operators we derive for these combinations and transformations are provably optimal, have linearity properties making them agnostic to the order of application, and are strongly analogous to the covariant transformations of natural gradients popular in the machine learning literature. The RMP framework enables the fusion of motion policies from different motion generation paradigms, such as dynamical systems, dynamic movement primitives (DMPs), optimal control, operational space control, nonlinear reactive controllers, motion optimization, and model predictive control (MPC), thus unifying these disparate techniques from the literature. RMPs are easy to implement and manipulate, facilitate controller design, simplify handling of joint limits, and clarify a number of open questions regarding the proper fusion of motion generation methods (such as incorporating local reactive policies into long-horizon optimizers). We demonstrate the effectiveness of RMPs on both simulation and real robots, including their ability to naturally and efficiently solve complicated collision avoidance problems previously handled by more complex planners.
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ReKep encodes robotic tasks as optimizable Python functions over 3D keypoints that are generated automatically from language and RGB-D input, enabling real-time hierarchical planning on single- and dual-arm platforms without task-specific data.
A 48-camera residential platform delivers real-time occlusion-robust 3D perception and coordinated actuation for multi-human multi-robot interaction in a shared home workspace.
Flow Motion Policy uses flow matching to model distributions over feasible manipulator paths, enabling best-of-N sampling with post-generation collision filtering to improve success and efficiency over prior neural and sampling-based planners.
VoxPoser uses LLMs to compose 3D value maps via VLM interaction for model-based synthesis of robust robot trajectories on open-set language-specified manipulation tasks.
SafePBDS uses pullback control barrier functions and a task manifold action interface to generate certifiably safe, steerable motions on high-DOF robots from objectives defined on arbitrary geometric spaces.
cuRoboV2 unifies B-spline optimization, GPU-native dense signed distance fields, and scalable whole-body kinematics and dynamics to achieve 99.7% success on payloaded manipulators and 99.6% collision-free IK on 48-DoF humanoids.
DexWild co-trains dexterous robot policies on in-the-wild human hand interactions recorded with a low-cost system and limited robot data, achieving 68.5% success in unseen environments and 5.8x better cross-embodiment generalization.
citing papers explorer
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Geometry-Aware Sampling-Based Motion Planning on Riemannian Manifolds
A sampling-based planner approximates Riemannian geodesic distances via midpoints with third-order accuracy and uses retractions plus natural gradients for local planning, producing lower-cost trajectories than Euclidean baselines on robotic arms and SE(2) systems.
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ReKep: Spatio-Temporal Reasoning of Relational Keypoint Constraints for Robotic Manipulation
ReKep encodes robotic tasks as optimizable Python functions over 3D keypoints that are generated automatically from language and RGB-D input, enabling real-time hierarchical planning on single- and dual-arm platforms without task-specific data.
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OmniRobotHome: A Multi-Camera Platform for Real-Time Multiadic Human-Robot Interaction
A 48-camera residential platform delivers real-time occlusion-robust 3D perception and coordinated actuation for multi-human multi-robot interaction in a shared home workspace.
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Flow Motion Policy: Manipulator Motion Planning with Flow Matching Models
Flow Motion Policy uses flow matching to model distributions over feasible manipulator paths, enabling best-of-N sampling with post-generation collision filtering to improve success and efficiency over prior neural and sampling-based planners.
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VoxPoser: Composable 3D Value Maps for Robotic Manipulation with Language Models
VoxPoser uses LLMs to compose 3D value maps via VLM interaction for model-based synthesis of robust robot trajectories on open-set language-specified manipulation tasks.
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Safe and Steerable Geometric Motion Policies for Robotic Dexterous Manipulation
SafePBDS uses pullback control barrier functions and a task manifold action interface to generate certifiably safe, steerable motions on high-DOF robots from objectives defined on arbitrary geometric spaces.
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cuRoboV2: Dynamics-Aware Motion Generation with Depth-Fused Distance Fields for High-DoF Robots
cuRoboV2 unifies B-spline optimization, GPU-native dense signed distance fields, and scalable whole-body kinematics and dynamics to achieve 99.7% success on payloaded manipulators and 99.6% collision-free IK on 48-DoF humanoids.
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DexWild: Dexterous Human Interactions for In-the-Wild Robot Policies
DexWild co-trains dexterous robot policies on in-the-wild human hand interactions recorded with a low-cost system and limited robot data, achieving 68.5% success in unseen environments and 5.8x better cross-embodiment generalization.