We present CCO-VOXEL: the very first chance-constrained optimization (CCO) algorithm that can compute trajectory plans with probabilistic safety guarantees in real-time directly on the voxel-grid representation of the world. CCO-VOXEL maps the distribution over the distance to the closest obstacle to a distribution over collision-constraint violation and computes an optimal trajectory that minimizes the violation probability. Importantly, unlike existing works, we never assume the nature of the sensor uncertainty or the probability distribution of the resulting collision-constraint violations. We leverage the notion of Hilbert Space embedding of distributions and Maximum Mean Discrepancy (MMD) to compute a tractable surrogate for the original chance-constrained optimization problem and employ a combination of A* based graph-search and Cross-Entropy Method for obtaining its minimum. We show tangible performance gain in terms of collision avoidance and trajectory smoothness as a consequence of our probabilistic formulation vis a vis state-of-the-art planning methods that do not account for such nonparametric noise. Finally, we also show how a combination of low-dimensional feature embedding and pre-caching of Kernel Matrices of MMD allows us to achieve real-time performance in simulations as well as in implementations on on-board commodity hardware that controls the quadrotor flight
翻译:我们展示了CCO-VOXEL:第一次机会限制优化(CCO)算法,它可以直接在对世界的 voxel-grid 代表处实时计算带有概率安全保障的轨迹计划。CCO-VOXEL 绘制了距离距离最接近的分布障碍的分布图,以尽可能减少违反碰撞限制规定的可能性。重要的是,与现有工作不同,我们从未假设传感器不确定性的性质或由此产生的碰撞限制违反的概率分布。我们利用Hilbert空间嵌入分布和最大平均值偏差的概念,为最初受机会限制的优化问题进行可移动的替代。CCO-VOXEL 绘制了距离距离最远的分布分布图,并计算出一个最佳的轨道,最大限度地减少违反的可能性。我们从避免碰撞和轨迹平滑看,这是我们相对于不考虑这种非分辨噪音的状态规划方法的预测性。我们利用了Hilbert Space 空间嵌入和最大平均值偏差(MMD)的概念来计算出一个可移动的替代装置。最后,我们还展示了基于A* 的图形搜索和跨轨道模型的模型,从而实现低空间飞行的软化的硬化的软操作,从而实现了KMDRO-RO-ROD-RO-RO-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-