Maximize-perturb-minimize: A fast and effective heuristic to obtain sets of locally optimal robot postures

Complex robots such as legged and humanoid robots are often characterized by non-convex optimization landscapes with multiple local minima. Obtaining sets of these local minima has interesting applications in global optimization, as well as in smart teleoperation interfaces with automatic posture suggestions. In this paper we propose a new heuristic method to obtain sets of local minima, which is to run multiple minimization problems initialized around a local maximum. The method is simple, fast, and produces diverse postures from a single nominal posture. Results on the robot WAREC-1 using a sum-of-squared-torques cost function show that our method quickly obtains lower-cost postures than typical random restart strategies. We further show that obtained postures are more diverse than when sampling around nominal postures, and that they are more likely to be feasible when compared to a uniform-sampling strategy. We also show that lack of completeness leads to the method being most useful when computation has to be fast, but not on very large computation time budgets.