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.
翻译:在本文中,我们建议对移动任务采用基于前向后向前向的分异方程式(FBSDE)的深度前向控制算法(FBSDE),我们还在FBSDE的配方中包括国家限制,以强制实施稳定的步行解决方案或人们可能希望考虑的其他制约因素(例如能源)。我们的方法使用深神经网络(即LSTM),一般地解决由所述最佳控制问题产生的高维汉密尔顿-贾科比-贝勒曼(HJB)等式。与传统方法相比,我们的拟议方法提供了更高的实时计算效率,从而产生了更频繁的闭路控制器。我们的方法的效力表现在线性倒转圆形行走模型(LIPM)上。尽管我们正在采用简化的行走模式,但该方法适用于机器人系统中的行走和其他控制/操作任务的一般和复杂模式。我们提供了模拟研究,以显示拟议方法的有效性。