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Yujun Dong

Publications and source records attributed to Yujun Dong.

3 recordsLinked to original sources

CHOREO: Every Humanoid Skill as a Trajectory

Recent advances in humanoid robotics have produced diverse skills through reinforcement learning, motion imitation, and generative modeling. Yet these capabilities remain siloed because they are built around incompatible representations, interfaces, and controllers. We present CHOREO, a framework for training-free composition of heterogeneous humanoid skills. Our key observation is that, regardless of how a skill is learned, it can ultimately be expressed as an executable motion trajectory. Based on this observation, CHOREO converts each capability into SkillMotion, a unified representation that combines motion states, contacts, semantics, and boundary conditions. Skills are composed through direct continuation, cubic Hermite blending, or validated bridge motions, without retraining source models or updating models at test time. On Unitree G1 in MuJoCo, CHOREO organizes 2,950 admitted SkillMotion assets derived from heterogeneous sources and achieves 95.4\% sequence success across 130 multi-action tasks, including 93.8\% success on eight-action sequences. These results demonstrate that executable trajectories provide a scalable interface for accumulating and composing pretrained humanoid capabilities.

cs.RO↗

Index theory for linear self-adjoint operator equations and nontrivial solutions for asymptotically linear operator equations(II)

Reference [1] established an index theory for a class of linear selfadjoint operator equations covering both second order linear Hamiltonian systems and first order linear Hamiltonian systems as special cases. In this paper based upon this index theory we construct a new reduced functional to investigate multiple solutions for asymptotically linear operator equations by Morse theory. The functional is defined on an infinite dimensional Hilbert space, is twice differentiable and has a finite Morse index. Investigating critical points of this functional by Morse theory gives us a unified way to deal with nontrivial solutions of both asymptotically second order Hamiltonian systems and asymptotically first order Hamiltonian systems.

math.CA↗

Index theory for linear self-adjoint operator equations and nontrivial solutions for asymptotically linear operator equations

We will first establish an index theory for linear self-adjoint operator equations. And then with the help of this index theory we will discuss existence and multiplicity of solutions for asymptotically linear operator equations by making use of the dual variational methods and Morse theory. Finally, some interesting examples concerning second order Hamiltonian systems, first order Hamiltonian systems and elliptical partial differential equations will be presented to illustrate our results.

math.CA↗