“Robust physics-based locomotion using low-dimensional planning” by Mordatch, De Lasa and Hertzmann

This paper presents a physics-based locomotion controller based on online planning. At each time-step, a planner optimizes locomotion over multiple phases of gait. Stance dynamics are modeled using a simplified Spring-Load Inverted (SLIP) model, while flight dynamics are modeled using projectile motion equations. Full-body control at each instant is optimized to match the instantaneous plan values, while also maintaining balance. Different types of gaits, including walking, running, and jumping, emerge automatically, as do transitions between different gaits. The controllers can traverse challenging terrain and withstand large external disturbances, while following high-level user commands at interactive rates.

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