Abstract: This paper applies trajectory-based optimization techniques to the synthesis of quadruped motions. The animator specifies hard constraints, consisting of footprint locations and their timings, and soft constraints that encode both physically-plausible behavior and the notion of comfortable positions. By dealing first and foremost with the spline trajectories representing the gross motion of the quadruped, the resulting optimization problem can be solved efficiently and robustly. Results include walking, jumping, and galloping quadrupeds.