where ( \mathbfM ) is a configuration-dependent inertia matrix and ( c_obs ) is a smooth barrier function.
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. hdmove2