Efficient Computation of Optimal, Physically Valid Motion

One appealing vision is that a user should be able to design a motion trajectory by setting a small number of keyframes and constraints—and that the resulting motion should remain optimal in some way. Variations of this problem have appeared in computer graphics, biomechanics, and robotics (e.g., [9] [6] [8] [7] [4]) Despite great interest and research progress, however, optimization is still viewed as impractical when the number of degrees of freedom is high; the reputation is that optimization will be slow, cumbersome, and difficult to guide toward a desired solution. To obtain motion for high degree of freedom characters using optimization, researchers in computer graphics, for example, have explored techniques ranging from extreme model simplification (e.g., [8]) to enforcing stereotypical momentum patterns [5] to discarding physical constraints entirely and relying on the animator to give the character a sense of weight and balance (e.g., [3]). We have found that physically plausible motion can be created for high degree of freedom characters by choosing to use only constraints and objective functions with derivatives that can be computed in time linear in the number of degrees of freedom of the character. Constraints that fall within this set include many of those used to enforce correct physics. For example, the swinging character in Figure 1 can apply very little torque about the bar axis, ground contact forces should fall within the friction cone at the feet, and linear and angular momentum should be conserved during the dismount. As the basis of our algorithm, we present a