We tackle the problem of trajectory planning in an environment comprised of a set of obstacles with uncertain time-varying locations. The uncertainties are modeled using widely accepted Gaussian distributions, resulting in a chance-constrained program. Contrary to previous approaches however, we do not assume perfect knowledge of the moments of the distribution, and instead estimate them through finite samples available from either sensors or past data. We derive tight concentration bounds on the error of these estimates to sufficiently tighten the chance-constraint program. As such, we provide provable guarantees on satisfaction of the chance-constraints corresponding to the nominal yet unknown moments. We illustrate our results with two autonomous vehicle trajectory planning case studies.

我们解决了在由一组具有不确定时变位置的障碍物组成的环境中的轨迹规划问题。使用广泛接受的高斯分布对不确定性进行建模，从而产生机会受限的程序。然而，与以前的方法相反，我们不假设对分布的矩有完美的了解，而是通过传感器或过去数据中可用的有限样本来估计它们。我们对这些估计的误差得出严格的集中界限，以充分收紧机会约束程序。因此，我们提供了满足与名义但未知时刻相对应的机会约束的可证明保证。我们用两个自动驾驶车辆轨迹规划案例研究来说明我们的结果。