To address the core issues of strong coupling of force and position in multi-robot suspension systems, failure of traditional algorithms in obstacle avoidance, and difficulty in balancing multiple objectives in multi-objective optimization, a force-position collaborative obstacle avoidance planning method guided by motion coupling is proposed. Firstly, the coupling characteristics of the multi-robot suspension system are analyzed, and the multi-robot coupling model is solved by the stepwise iterative coordinated solution strategy. Secondly, the force-position mapping matrix is constructed to describe the coupling relationship between tension and position, and the force-position coordinated constraint equation is established based on the principle of mechanical equilibrium. Then, the hierarchical search and stepwise optimization strategy is proposed, which decomposes the complex problem into two sub-problems of global trajectory planning and local force-position optimization, achieving the efficient integration of force-position coordinated planning and obstacle avoidance. Then, the FLA-MGEA fusion algorithm is designed. MGEA (Multi-strategy Geyser-Inspired Algorithm) effectively avoids the algorithm falling into local optimum by introducing chaotic mapping initialization, Lévy flight optimization and stability constraint conditions; FLA (Fuzzy Logic Algorithm) dynamically adjusts the weight of the optimization objective according to the complexity of the environment. Finally, the dynamic obstacle avoidance experiment verifies the performance of the obstacle avoidance planning method in terms of force-position coordinated accuracy and obstacle avoidance reliability. The research results lay a theoretical foundation for the engineering application of the hybrid-drive suspension system.