Author: Dr. A. Sterling Affiliation: Institute for Computational Kinematics, University of Neural Systems Date: April 14, 2026 Abstract This paper introduces hdmove2 , a novel computational framework for high-dimensional movement synthesis and trajectory optimization in real-time kinematic systems. Unlike conventional motion planning algorithms that suffer from the "curse of dimensionality" in spaces exceeding 12 degrees of freedom (DoF), hdmove2 leverages a hybrid approach combining Riemannian manifold learning with a sparse, event-driven update rule. The framework is designed for applications ranging from robotic manipulators with 50+ DoF to full-body humanoid locomotion. We present the core architecture, the mathematical formulation of the hdmove2 kernel, benchmarking results against state-of-the-art algorithms (RRT*, CHOMP, and TrajOpt), and a case study in real-time obstacle negotiation. Our results demonstrate a 74% reduction in cumulative jerk, a 40% improvement in convergence speed, and robust performance in up to 128-dimensional configuration spaces. 1. Introduction Movement in high-dimensional spaces remains a fundamental challenge in robotics, biomechanics, and computer animation. Traditional motion planners—such as Rapidly-exploring Random Trees (RRT*) and Covariant Hamiltonian Optimization for Motion Planning (CHOMP)—exhibit polynomial-to-exponential runtime scaling as the number of degrees of freedom (DoF) increases [1], [2]. For systems beyond 20 DoF, these methods often fail to meet real-time constraints.
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[ z^* = \arg\min_z(t) \in Z \mathcalJ[D(z(t))] \quad \texts.t. \quad \texthomotopy constraints ] hdmove2
[2] N. Ratliff, M. Zucker, J. A. Bagnell, and S. Srinivasa, "CHOMP: Gradient optimization algorithms for efficient motion planning," IEEE International Conference on Robotics and Automation (ICRA) , 2009, pp. 1292–1299.
[3] A. Sterling and J. Liu, "hdmove1: Latent motion primitives for high-DoF planning," arXiv preprint arXiv:2401.04567 , 2024. Author: Dr
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| Algorithm | Success Rate (Bench B) | Planning Time (ms) | Cumulative Jerk (m²/s⁵) | Real-time feasible (>30 Hz) | |-----------|------------------------|--------------------|--------------------------|-------------------------------| | RRT* | 0.12 ± 0.05 | 3420 ± 450 | 18.4 ± 3.2 | No | | CHOMP | 0.68 ± 0.12 | 520 ± 85 | 9.2 ± 1.8 | No (for n>30) | | hdmove1 | 0.71 ± 0.10 | 88 ± 12 | 5.3 ± 0.9 | Yes (at 35 Hz) | | | 0.94 ± 0.04 | 41 ± 6 | 1.4 ± 0.3 | Yes (at 95 Hz) | Our results demonstrate a 74% reduction in cumulative
The lower level is solved using a fast alternating direction method of multipliers (ADMM) that converges in under 5 ms for ( n \leq 128 ). Re-planning is triggered when: