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Various constraints exist in bipedal movement. Due to the natural ability of effectively handling constraints, trajectory optimization has become one of the mainstream methods in biped gait planning, especially when constraints become much more complex on non-flat terrain. In this paper, we propose a multi-modal biped gait planner based on DIRCON, which can generate different gaits for multiple, non-flat terrains. Firstly, a virtual knot is designed to model the state transitions when the swing foot contacts terrain and is inserted as the first knot of the target trajectory of the current support phase. Thus, a complete gait or multi-modal gaits sequence can be generated at one time. Then, slacked complementary constraints, which can avoid undesired trajectories, are elaborated to describe the coupling relationships between terrain information and bipedal motion for trajectory optimization based gait planning. The concrete form of the gait planner is also delivered. Finally, we verify the performance of the planner, as well as the structural design of our newly designed biped robot in CoppeliaSim through flat terrain walking, stairs terrain walking and quincuncial piles walking. The three experiments show that the gaits planned by the proposed planner can enable the robot to walk stably over non-flat terrains, even through simple PD control. [ABSTRACT FROM AUTHOR]