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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Riemannian Motion Policies
13 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.
TempoVLA learns a single VLA policy with controllable execution speed via variable-speed trajectory augmentation and explicit speed conditioning.
Introduces world-task factorization for robot policies using Bayesian evidence and AICON graph plus learned modulator, outperforming baselines with zero-shot generalization in heterogeneous robotics settings.
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.
OptiWorld inserts a classical optimal-control layer that extracts a world state, plans an optimal trajectory on a geometric manifold under physical constraints, and renders the video conditioned on that trajectory.
Nullspace projections on a graph-based model enable reactive control to achieve 100% success in non-convex planar pushing across 100 configurations, versus 0% for steepest descent and ~55% for diffusion policy, without training or retraining.
GAM framework uses arc-length parameterization for temporal invariance and schema-affine factorization for geometric invariance to build a covariant action manifold integrated into VLA models for improved generalization from sparse data.
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OptiWorld: Optimal Control for Video World Generation under Physical Constraints
OptiWorld inserts a classical optimal-control layer that extracts a world state, plans an optimal trajectory on a geometric manifold under physical constraints, and renders the video conditioned on that trajectory.
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General Covariant Action Modeling: Constructing Generalized Manifolds via Spatio-Temporal Decoupling
GAM framework uses arc-length parameterization for temporal invariance and schema-affine factorization for geometric invariance to build a covariant action manifold integrated into VLA models for improved generalization from sparse data.