  In this paper, we propose a deep forward-backward stochastic differential
equation (FBSDE) based control algorithm for locomotion tasks. We also include
state constraints in the FBSDE formulation to impose stable walking solutions
or other constraints that one may want to consider (e.g., energy). Our approach
utilizes a deep neural network (i.e., LSTM) to solve, in general,
high-dimensional Hamilton-Jacobi-Bellman (HJB) equation resulting from the
stated optimal control problem. As compared to traditional methods, our
proposed method provides a higher computational efficiency in real-time; thus
yielding higher frequency implementation of the closed-loop controllers. The
efficacy of our approach is shown on a linear inverted pendulum model (LIPM)
for walking. Even though we are deploying a simplified model of walking, the
methodology is applicable to generalized and complex models for walking and
other control/optimization tasks in robotic systems. Simulation studies have
been provided to show the effectiveness of the proposed methodology.
