Quantifying the trade-offs between stability versus energy use for underactuated biped walking

In this paper, we address the problem of incorporating both energy consumption and stability into a cost function for bipedal walking. To solve the problem, we also propose a basic framework and demonstrate its effectiveness in simulation. This framework allows one to use a scalar coefficient to adjust the trade-off between stability and energy use. The optimal scalar value depends on the robot, terrain, task and priorities. In order to implement the methods in this paper, multiple low-level walking controllers and meshing of a ten-dimensional state space are needed. This latter requirement would normally be impractical for a 10D system; however, we exploit the observation that our low-level controllers cause the step-to-step dynamics to fill only a small, quasi-2D region, thus enabling meshing and, correspondingly, dynamic programming based on the resulting Markov Decision Process (MDP). Both the introduction of the energy/stability trade-off problem and our proposed framework for its solution have potential for significant utility in the future, as robot locomotion is developed to operate in increasingly less structured (stochastic) environments.