Traditional manual inspection and operational maintenance methods for industrial equipment and infrastructure face multifaceted technical challenges. Although robots demonstrate superior operational efficiency and safety compared to human operators, existing solutions remain limited by inadequate reachability and insufficient structural compactness. To solve this problem, inspired by the coiling behavior of arboreal snakes, a multi-coiled cable-driven robot (MC-CDR) with enhanced structural compactness and excellent exploration reachability is designed. The robot consists of a rotating platform, six fully constrained rigid links driven by double-cable synchronous traction module, and a rotating base. A multi-level kinematics mapping framework is established to express complex motion relationships. A variable degree-of-freedom kinematic model (VDOFKM) is developed to solve the motion interference problem of the coiled redundant robot by dynamically determining the minimum number of activated joints. Based on the VDOFKM, a multi-constraint motion planning (MCMP) method is proposed to realize global path planning in complex environments, which integrates joint constraints, base constraints and obstacle avoidance constraints. Simulation results demonstrate that MCMP achieves superior computational efficiency, smoother joint configurations, and less motion compared to conventional methods. Additionally, the MCMP enables continuous collision-free joint configurations acquisition during path tracking. The prototype experiments validate that the integration of VDOFKM and MCMP equips MC-CDR with higher solution efficiency, excellent environmental reachability and maneuverability in complex environments.