Hdmove2 |verified| May 2026
[ \mathcalJ[\tau] = \int_0^T \left( \underbrace \textkinetic energy + \lambda_1 \underbrace \textjerk + \lambda_2 \underbracec_obs(\tau(t))_\textcollision cost \right) dt ]
[ z^* = \arg\min_z(t) \in Z \mathcalJ[D(z(t))] \quad \texts.t. \quad \texthomotopy constraints ] hdmove2
[ \exists t: | q_actual(t) - \tau_planned(t) | > \sigma \cdot \textVar s \in [t-\delta,t] \left[ \frac\partial c obs\partial q(s) \right] ] Ratliff, M
where ( \mathbfM ) is a configuration-dependent inertia matrix and ( c_obs ) is a smooth barrier function. Instead of solving directly in ( Q ), hdmove2 solves: Bagnell, and S
[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.
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.
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:
