RRT * -Based Full State Constrained Motion Planning for 7-DOF Overhead Crane With Obstacle Avoidance

The underactuated 7-degrees of freedom (DOF) overhead cranes exhibit complex double-spherical-pendulum dynamics with time-varying cable lengths, which complicates simultaneous achievement of precise positioning, swing suppression, and obstacle avoidance. This article proposes an rapidly-exploring random trees star (RRT${^{\boldsymbol{\ast}}}$)-based motion planning strategy that effectively addresses these challenges by ensuring full-state constraint satisfaction while optimizing transportation time. The framework first establishes a novel dynamic model incorporating cable-length variations and double pendulum effects, then formulates the motion planning as a constrained optimization problem with coupled state variables. A modified RRT${^{\boldsymbol{\ast}}}$algorithm with adaptive sampling is developed to handle the high-dimensional state space while respecting actuator limits and swing constraints. The proposed method uniquely integrates auxiliary signal design with sampling-based planning to generate collision-free trajectories for the payload. The proposed method delivers markedly superior performance over existing methods, achieving a 29.88$\boldsymbol{\%}$faster transportation and a 50.00$\boldsymbol{\%}$lower payload swing, along with reliable obstacle avoidance in complex 3-D environments.