Optimal control is often used in robotics for planning a trajectory to achieve some desired behavior, as expressed by the cost function. Most works in optimal control focus on finding a single optimal trajectory, which is then typically tracked by another controller. In this work, we instead consider trajectory distribution as the solution of an optimal control problem, resulting in better tracking performance and a more stable controller. A Gaussian distribution is first obtained from an iterative Linear Quadratic Regulator (iLQR) solver. A short horizon Model Predictive Control (MPC) is then used to track this distribution. We show that tracking the distribution is more cost-efficient and robust as compared to tracking the mean or using iLQR feedback control. The proposed method is validated with kinematic control of 7-DoF Panda manipulator and dynamic control of 6-DoF quadcopter in simulation.
翻译:优化控制常常用于机器人中规划轨迹以实现某种理想行为,如成本函数所示。大多数在最佳控制中的工作重点是寻找单一的最佳轨迹,然后通常由另一个控制者跟踪。在这项工作中,我们把轨迹分布视为最佳控制问题的解决办法,从而更好地跟踪性能和更稳定的控制器。首先从迭接线性二次二次曲线调节(iLQR)解答器获得高斯分布。然后使用短期模型预测控制(MPC)来跟踪这一分布。我们表明,跟踪分布比跟踪平均值或使用iLQR反馈控制更具成本效益和稳健性。在模拟中,对7-DoF Panda操纵器和6-DoF四重机动态控制进行动态控制,从而验证了拟议方法。