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Previous studies on Connected and Automated Vehicles (CAVs) demonstrated the potential to coordinate the behaviors of multiple connected vehicles for traffic improvements. In this paper, we first propose a Conflict Duration Graph-based (CDG-based) coordination framework to resolve collisions and improve the traffic capacity of signal-free intersections. Secondly, a Speed Control-based Intersection Coordination Model (SICM) is developed to identify complex constraints in multi-vehicle collision scenarios. Thirdly, a geometric Translation-based Intersection Coordination Algorithm (TICA) is proposed to calculate the ideal location of time blocks in CDGs and then obtain the near-optimal design speed in the form of combinatorial optimization. Twelve groups of test scenarios with different traffic volumes were designed and tested on a MATLAB-based simulation platform. Simulation results showed that the proposed method can resolve all the collisions and instruct the vehicles to pass signal-free intersections collaboratively without stopping in low to medium level of congestion.