In this paper, we consider the closed-loop control problem of nonlinear
robotic systems in the presence of probabilistic uncertainties and
disturbances. More precisely, we design a state feedback controller that
minimizes deviations of the states of the system from the nominal state
trajectories due to uncertainties and disturbances. Existing approaches to
address the control problem of probabilistic systems are limited to particular
classes of uncertainties and systems such as Gaussian uncertainties and
processes and linearized systems. We present an approach that deals with
nonlinear dynamics models and arbitrary known probabilistic uncertainties. We
formulate the controller design problem as an optimization problem in terms of
statistics of the probability distributions including moments and
characteristic functions. In particular, in the provided optimization problem,
we use moments and characteristic functions to propagate uncertainties
throughout the nonlinear motion model of robotic systems. In order to reduce
the tracking deviations, we minimize the uncertainty of the probabilistic
states around the nominal trajectory by minimizing the trace and the
determinant of the covariance matrix of the probabilistic states. To obtain the
state feedback gains, we solve deterministic optimization problems in terms of
moments, characteristic functions, and state feedback gains using off-the-shelf
interior-point optimization solvers. To illustrate the performance of the
proposed method, we compare our method with existing probabilistic control
methods.

该论文提出了一种针对非线性机器人系统中存在的概率不确定性和干扰的闭环控制问题的解决方案，并将控制器设计问题作为概率分布的统计量的优化问题来处理，以此来降低跟踪偏差，并通过与现有的概率控制方法的比较来证明其性能。