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This paper introduces , 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. hdmove2
where ( \sigma ) is a sensitivity parameter. This ensures computational resources are focused only on dynamically relevant periods. Here is a review of the tool based
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 framework is designed for applications ranging from
Data flow: Sensor input → LTP (latent planning) → GS (lifting & projection) → EDC (execution & monitoring) → Control signals.
hdmove1 introduced the concept of "latent motion primitives" (LMPs) – a 12-dimensional manifold embedded in the high-dimensional configuration space. However, reconstruction errors led to dynamic infeasibility during high-speed maneuvers, motivating the development of hdmove2 .