### Summary

This paper discusses a new way of animating characters. Rather than specifying the poses of a character at key frames in the animation, the authors wish to specify what the character should do at a high level. Their system then determines several physically plausible trajectories and selects the "best" one.

However, there are some complications. First, it is necessary to provide a proper model for the character. Correctly modelling a character in a physical sense can be extraordinarily difficult. The character used in the paper, a Luxo lamp, was modeled as a set of rigid segments hinged at joints, with springs at the joints. This model is incredibly simplistic as opposed to a model that would be necessary for simulating, say, human motion or the motion of an animal. Next there is the issue of how to determine which physically correct motion is the best one. This is determined by trying to optimize some metric, for example, attempting to minimize the amount of energy expended in performing an action. Finally, there is the problem of solving this non-linear, constrained optimization problem. To solve this problem, the authors employ the Sequential Quadratic Programming method. 

They produce a variety of results that show a Luxo lamp performing various actions. The results are quite impressive.