This paper presents a trajectory optimization algorithm for legged robotics that uses a novel cost function incorporating point cloud data to simultaneously optimize for footstep locations and center of mass trajectories. This novel formulation transforms the inherently discrete problem of selecting footstep locations into a continuous cost. The algorithm seamlessly balances the desire to choose footstep locations that enhance the dynamic performance of the robot while still choosing locations that are viable and safe. We demonstrate the success of this algorithm by navigating the ALPHRED V2 robotic system over unknown terrain in a simulation environment.

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