Embedding Hybrid Systems into Continuous Latent Vector Fields

This work proves that an $n$-dimensional hybrid system can be embedded into an $m$-dimensional Euclidean space equipped with a continuous vector field on its embedded image whenever $m>2n$. This result suggests that an intrinsically discontinuous hybrid system generically admits a continuous extrinsic representation that is well-posed for differentiable optimization. Building on this existence theorem, we show that a latent Neural ODE with consistency loss in both the latent and state space can accurately recover the flow of hybrid systems. Extensive experiments suggest the proposed method outperforms the existing method in learning hybrid systems with varying geometries from only time series data.

LieIPM: Lie Group Interior Point Method for Direct Trajectory Optimization of Rigid Bodies

Designing dynamically feasible trajectories for rigid bodies is a fundamental problem in robotics. While direct methods are widely used, the existing constrained optimizers typically operate in Euclidean space and ignore the manifold structure of rigid body motions. This mismatch may introduce singularities or lead to poorly conditioned optimization problems. To bridge this gap, we develop a structure-aware framework for constrained trajectory optimization directly on matrix Lie groups. Our approach is based on the second-order rigid body models utilizing Lie group structures, which enables efficient Newton-type updates while preserving the underlying geometry. Building on this model, we propose a line-search Lie Group Interior Point Method (LieIPM) to handle constraints on the manifolds. We instantiate the framework for rigid body motion planning using Lie group variational integrators and derive closed-form intrinsic derivatives that exploit group symmetries. The LieIPM preserves the topology of rotation motions by construction and avoids singularities. Numerical results demonstrate superior robustness and faster convergence compared to general-purpose solvers and structure-exploiting optimal control methods.

LadderMan: Learning Humanoid Perceptive Ladder Climbing

Humanoid robots hold great promise for operating in human-centered environments, yet ladder climbing remains one of the most challenging tasks due to sparse footholds and handholds, complex whole-body coordination, and sensitivity to perception and control errors. We present \textbf{LadderMan}, a unified system that enables humanoid robots to robustly climb diverse ladders and perform manipulation under such constrained conditions. Our climbing policy is built on a scalable two-stage learning pipeline, where we use hybrid motion tracking to learn multiple climbing experts from a single reference motion, and distill these experts into a unified depth-based visuomotor climbing policy via hybrid imitation and reinforcement learning. To enable real-world deployment, we leverage vision foundation models to bridge the sim-to-real gap in depth perception. Building on the learned climbing policy, we further train a separate manipulation policy using a dual-agent formulation, allowing stable on-ladder manipulation via teleoperation. Experiments demonstrate that LadderMan achieves robust ladder climbing across a wide range of geometries, successfully transfers to real-world hardware in a zero-shot manner, and supports various manipulation tasks under challenging ladder constraints. Video results are available at https://ladderman-robot.github.io .

Robust Adversarial Policy Optimization Under Dynamics Uncertainty

Reinforcement learning (RL) policies often fail under dynamics that differ from training, a gap not fully addressed by domain randomization or existing adversarial RL methods. Distributionally robust RL provides a formal remedy but still relies on surrogate adversaries to approximate intractable primal problems, leaving blind spots that potentially cause instability and over-conservatism. We propose a dual formulation that directly exposes the robustness-performance trade-off. At the trajectory level, a temperature parameter from the dual problem is approximated with an adversarial network, yielding efficient and stable worst-case rollouts within a divergence bound. At the model level, we employ Boltzmann reweighting over dynamics ensembles, focusing on more adverse environments to the current policy rather than uniform sampling. The two components act independently and complement each other: trajectory-level steering ensures robust rollouts, while model-level sampling provides policy-sensitive coverage of adverse dynamics. The resulting framework, robust adversarial policy optimization (RAPO) outperforms robust RL baselines, improving resilience to uncertainty and generalization to out-of-distribution dynamics while maintaining dual tractability.

A Ray Intersection Algorithm for Fast Growth Distance Computation Between Convex Sets

In this paper, we discuss an efficient algorithm for computing the growth distance between two compact convex sets with representable support functions. The growth distance between two sets is the minimum scaling factor such that the sets intersect when scaled about some center points. Unlike the minimum distance between sets, the growth distance provides a unified measure for set intersection and separation. We first reduce the growth distance problem to an equivalent ray intersection problem on the Minkowski difference set. Then, we propose an algorithm to solve the ray intersection problem by iteratively constructing inner and outer polyhedral approximations of the Minkowski difference set. We show that our algorithm satisfies several key properties, such as primal and dual feasibility and monotone convergence. We provide extensive benchmark results for our algorithm and show that our open-source implementation achieves state-of-the-art performance across a wide variety of convex sets. Finally, we demonstrate robotics applications of our algorithm in motion planning and rigid-body simulation.

WOMBET: World Model-based Experience Transfer for Robust and Sample-efficient Reinforcement Learning

Reinforcement learning (RL) in robotics is often limited by the cost and risk of data collection, motivating experience transfer from a source task to a target task. Offline-to-online RL leverages prior data but typically assumes a given fixed dataset and does not address how to generate reliable data for transfer. We propose \textit{World Model-based Experience Transfer} (WOMBET), a framework that jointly generates and utilizes prior data. WOMBET learns a world model in the source task and generates offline data via uncertainty-penalized planning, followed by filtering trajectories with high return and low epistemic uncertainty. It then performs online fine-tuning in the target task using adaptive sampling between offline and online data, enabling a stable transition from prior-driven initialization to task-specific adaptation. We show that the uncertainty-penalized objective provides a lower bound on the true return and derive a finite-sample error decomposition capturing distribution mismatch and approximation error. Empirically, WOMBET improves sample efficiency and final performance over strong baselines on continuous control benchmarks, demonstrating the benefit of jointly optimizing data generation and transfer.

SPARK: Skeleton-Parameter Aligned Retargeting on Humanoid Robots with Kinodynamic Trajectory Optimization

Human motion provides rich priors for training general-purpose humanoid control policies, but raw demonstrations are often incompatible with a robot's kinematics and dynamics, limiting their direct use. We present a two-stage pipeline for generating natural and dynamically feasible motion references from task-space human data. First, we convert human motion into a unified robot description format (URDF)-based skeleton representation and calibrate it to the target humanoid's dimensions. By aligning the underlying skeleton structure rather than heuristically modifying task-space targets, this step significantly reduces inverse kinematics error and tuning effort. Second, we refine the retargeted trajectories through progressive kinodynamic trajectory optimization (TO), solved in three stages: kinematic TO, inverse dynamics, and full kinodynamic TO, each warm-started from the previous solution. The final result yields dynamically consistent state trajectories and joint torque profiles, providing high-quality references for learning-based controllers. Together, skeleton calibration and kinodynamic TO enable the generation of natural, physically consistent motion references across diverse humanoid platforms.

Perceptive Humanoid Parkour: Chaining Dynamic Human Skills via Motion Matching

While recent advances in humanoid locomotion have achieved stable walking on varied terrains, capturing the agility and adaptivity of highly dynamic human motions remains an open challenge. In particular, agile parkour in complex environments demands not only low-level robustness, but also human-like motion expressiveness, long-horizon skill composition, and perception-driven decision-making. In this paper, we present Perceptive Humanoid Parkour (PHP), a modular framework that enables humanoid robots to autonomously perform long-horizon, vision-based parkour across challenging obstacle courses. Our approach first leverages motion matching, formulated as nearest-neighbor search in a feature space, to compose retargeted atomic human skills into long-horizon kinematic trajectories. This framework enables the flexible composition and smooth transition of complex skill chains while preserving the elegance and fluidity of dynamic human motions. Next, we train motion-tracking reinforcement learning (RL) expert policies for these composed motions, and distill them into a single depth-based, multi-skill student policy, using a combination of DAgger and RL. Crucially, the combination of perception and skill composition enables autonomous, context-aware decision-making: using only onboard depth sensing and a discrete 2D velocity command, the robot selects and executes whether to step over, climb onto, vault or roll off obstacles of varying geometries and heights. We validate our framework with extensive real-world experiments on a Unitree G1 humanoid robot, demonstrating highly dynamic parkour skills such as climbing tall obstacles up to 1.25m (96% robot height), as well as long-horizon multi-obstacle traversal with closed-loop adaptation to real-time obstacle perturbations.

RPL: Learning Robust Humanoid Perceptive Locomotion on Challenging Terrains

Humanoid perceptive locomotion has made significant progress and shows great promise, yet achieving robust multi-directional locomotion on complex terrains remains underexplored. To tackle this challenge, we propose RPL, a two-stage training framework that enables multi-directional locomotion on challenging terrains, and remains robust with payloads. RPL first trains terrain-specific expert policies with privileged height map observations to master decoupled locomotion and manipulation skills across different terrains, and then distills them into a transformer policy that leverages multiple depth cameras to cover a wide range of views. During distillation, we introduce two techniques to robustify multi-directional locomotion, depth feature scaling based on velocity commands and random side masking, which are critical for asymmetric depth observations and unseen widths of terrains. For scalable depth distillation, we develop an efficient multi-depth system that ray-casts against both dynamic robot meshes and static terrain meshes in massively parallel environments, achieving a 5-times speedup over the depth rendering pipelines in existing simulators while modeling realistic sensor latency, noise, and dropout. Extensive real-world experiments demonstrate robust multi-directional locomotion with payloads (2kg) across challenging terrains, including 20° slopes, staircases with different step lengths (22 cm, 25 cm, 30 cm), and 25 cm by 25 cm stepping stones separated by 60 cm gaps.

mjlab: A Lightweight Framework for GPU-Accelerated Robot Learning

We present mjlab, a lightweight, open-source framework for robot learning that combines GPU-accelerated simulation with composable environments and minimal setup friction. mjlab adopts the manager-based API introduced by Isaac Lab, where users compose modular building blocks for observations, rewards, and events, and pairs it with MuJoCo Warp for GPU-accelerated physics. The result is a framework installable with a single command, requiring minimal dependencies, and providing direct access to native MuJoCo data structures. mjlab ships with reference implementations of velocity tracking, motion imitation, and manipulation tasks.