viewpoint self-motion parameterization

This work addresses the challenge of real-time motion planning for complex robotic systems under geometric constraints, which is often hindered by high computational costs. For the first time, SIMD parallelization is introduced into manifold-constrained motion planning by reformulating projection operations into a parallelizable structure that leverages CPU SIMD instruction sets to efficiently accelerate constraint satisfaction. The proposed method dramatically improves computational efficiency, enabling real-time whole-body quasi-static motion planning on a physical humanoid robot. Experimental results demonstrate speedups of 100 to 1,000 times compared to existing approaches, while maintaining accuracy and feasibility under stringent geometric constraints.

This work addresses the challenge of nonlinear optimization with mixed equality and inequality constraints in robotic dynamics planning by introducing a novel approach based on “constraint manifolds with corners.” The method reformulates the original problem as an unconstrained optimization over a constrained state space, seamlessly embedding inequality constraints into the manifold structure through differential geometry and manifold optimization techniques. This formulation overcomes the conventional limitation of manifold optimization, which typically applies only to smooth equality constraints. Evaluated on large-scale dynamic planning tasks, the proposed approach successfully generates dynamically feasible trajectories and demonstrates superior robustness and solvability in scenarios where standard algorithms fail.

To address the challenge of real-time motion planning for high-dimensional dynamical systems in dynamic environments, this paper proposes a two-stage framework: offline construction of a low-dimensional trajectory manifold followed by online gradient-based optimization within the manifold. The key contribution is the introduction of Differentiable Motion Manifold Primitives (DMMPs)—a novel model that implicitly represents continuous-time, differentiable trajectories as low-dimensional manifolds, enabling end-to-end training and explicit embedding of dynamical constraints. The method integrates neural network modeling, manifold learning, and gradient-based online optimization. Evaluated on a 7-DOF robotic arm performing dynamic throwing, the approach achieves a 3.2× speedup in planning time, a 27% improvement in task success rate, and a 99.8% constraint satisfaction rate—demonstrating substantial gains in reactivity and environmental adaptability.

This work addresses the suboptimality of motion plans in robotics that arises from neglecting the non-Euclidean geometric structure of configuration spaces. To this end, we propose a sampling-based planning framework that operates directly on Riemannian manifolds. Our method efficiently approximates Riemannian geodesic distances using a third-order accurate midpoint scheme and, for the first time, integrates Riemannian natural gradients with first-order retraction operations into local path generation. This approach preserves geometric fidelity while ensuring scalability to high-dimensional systems. Experimental results demonstrate that our planner consistently produces trajectories with significantly lower cost—measured under the kinetic energy metric—than both Euclidean planners and conventional numerical geodesic solvers across diverse platforms, including a planar two-link arm, a 7-DoF Franka manipulator, and an SE(2) nonholonomic system.

This work addresses the challenge of globally characterizing the geometric structure of solution manifolds in redundant robotic tasks, which exhibit non-uniqueness and form continuous manifolds in configuration space. Existing approaches struggle to capture these structures comprehensively. The paper proposes a representation-centric implicit modeling paradigm that constructs a scalar field over the configuration space, whose zero-level set precisely coincides with the task-induced solution manifold. By integrating Jacobian-guided neighborhood sampling with implicit neural representations, the method learns a signed distance field of the solution manifold, enabling globally consistent and continuous modeling under arbitrary task mappings—a capability demonstrated for the first time. Experiments on a planar three-link robot and a seven-degree-of-freedom Franka manipulator validate the approach’s ability to accurately reconstruct solution manifolds and generalize across varying task parameters.

This work addresses the challenge of motion planning in tightly fitted rigid-body assembly, where near-zero clearance contact imposes strong geometric constraints. To tackle this problem, we propose CMG-RRT, an algorithm that, for the first time, incorporates the critical manifold—the set of contact configurations between parts—as a guiding mechanism within a sampling-based planner. By adaptively biasing sampling toward neighborhoods of this manifold in configuration space and integrating a hierarchical subdivision strategy within the RRT framework, CMG-RRT efficiently explores feasible assembly paths. The algorithm achieves a 100% success rate on a challenging rotational assembly benchmark and, notably, provides the first fully automatic solution to the Elk interlocking puzzle. The implementation is publicly available.

This work investigates whether diffusion models can learn and recover the intrinsic geometric structure of data manifolds without prior knowledge. To this end, the authors construct a controlled experimental setting based on constrained inverse kinematics (IK), where task-space constraints define configuration manifolds with known dimensions and analytical solutions. Conditional diffusion models are trained in this setting and evaluated on UR5 and Franka robotic platforms across seven families of constraints. Through analyses of score functions, linear interpolation in latent space, and intrinsic dimension estimation, the study demonstrates that the recovered intrinsic dimensions align closely with theoretical degrees of freedom, and interpolated trajectories remain near the constraint manifolds. These findings provide the first empirical validation that diffusion models can effectively learn complex geometric structures and exhibit a meaningful geometric inductive bias.

This work addresses the suboptimality in global execution time arising from the decoupling of path planning and joint configuration in multi-view robotic inspection. To overcome this limitation, the authors propose a unified optimization framework that jointly determines the visiting sequence of multiple 6-DoF inspection poses and the corresponding inverse kinematics solutions for a 9-DoF robot. By co-optimizing the visitation order and joint configurations on the three-dimensional self-motion manifold, the approach circumvents the inherent suboptimality of conventional modular pipelines and reduces trajectory computation complexity from quadratic to linear. The method integrates closed-form parameterization of the self-motion manifold, a double-integrator proxy model, random-key encoding, gradient-free CMA-ES optimization, and edge-wise direct collocation. Experiments on a KUKA LBR iiwa robot demonstrate that the generated trajectories are collision-free, smooth, and time-optimal, achieving significantly shorter end-to-end inspection times compared to modular and distance-based baselines.

Existing methods for automatic rigging of 3D meshes often fail to model plausible joint pose distributions effectively, leading to anatomically implausible or geometrically self-intersecting poses. This work proposes ViPS, a framework that, for the first time, distills motion priors from pretrained 2D video diffusion models into a general-purpose 3D pose distribution, enabling zero-shot generalization to unseen species and skeletal topologies without relying on scarce 4D data. By integrating a differentiable geometric validator with latent-space pose modeling, ViPS supports effective pose sampling, inverse kinematics projection, and temporally coherent keyframe generation. Experiments demonstrate that ViPS, trained solely on video priors, matches state-of-the-art methods based on synthetic 4D data in both pose plausibility and diversity, while exhibiting superior cross-domain generalization capabilities.