论文标题
在系统不确定性下具有非线性安全限制的差异动态编程
Differential Dynamic Programming with Nonlinear Safety Constraints Under System Uncertainties
论文作者
论文摘要
诸如机器人之类的系统的安全操作要求他们计划和执行受安全限制的轨迹。当这些系统在动态中受到不确定性的影响时，确保不违反约束的问题是一项挑战。在本文中，我们提出了Safe-CDP，这是基于约束差分动态编程（DDP）的添加剂不确定性和非线性安全限制的安全轨迹优化和控制方法。机器人在其运动过程中的安全性被制定为具有限制满意度的用户选择概率的机会限制。通过约束拧紧，在DDP公式中，机会限制被转化为确定性的限制。为了避免在约束收紧过程中过度保守性，使用约束DDP得出的反馈策略的线性控制收益用于预测中闭环不确定性传播的近似。在三种不同的机器人动力学上，对所提出的算法进行了经验评估，模拟的自由度最高。通过物理硬件实现证明了该方法的计算可行性和适用性。
Safe operation of systems such as robots requires them to plan and execute trajectories subject to safety constraints. When those systems are subject to uncertainties in their dynamics, it is challenging to ensure that the constraints are not violated. In this paper, we propose Safe-CDDP, a safe trajectory optimization and control approach for systems under additive uncertainties and non-linear safety constraints based on constrained differential dynamic programming (DDP). The safety of the robot during its motion is formulated as chance constraints with user-chosen probabilities of constraint satisfaction. The chance constraints are transformed into deterministic ones in DDP formulation by constraint tightening. To avoid over-conservatism during constraint tightening, linear control gains of the feedback policy derived from the constrained DDP are used in the approximation of closed-loop uncertainty propagation in prediction. The proposed algorithm is empirically evaluated on three different robot dynamics with up to 12 degrees of freedom in simulation. The computational feasibility and applicability of the approach are demonstrated with a physical hardware implementation.
