CCO-VOXEL: Chance Constrained Optimization over Uncertain Voxel-Grid Representation for Safe Trajectory Planning

Abstract

Fig. 1: Overview: Accurate gradient and distance to closest obstacles cannot be extracted from uncertain voxel grid representation built from noisy sensors. Fig.(a) illustrates this effect, wherein the gradient at a given point can be in any one of the directions shown by arrows.Similarly, the distribution of distance is shown as a confidence interval band. The noisy gradients and distance estimation tend to guide the trajectory towards the obstacle leading to a collision as shown in (b) (the collision is highlighted by a white circle) . We propose CCO-VOXEL, a method that accounts for the uncertainty in the distance measurements and obtains an optimal solution through a gradient free Cross Entropy Minimization technique resulting in a safe and optimal trajectories as shown in (c).

Leveraging Distributional Bias for Reactive Collision Avoidance under Uncertainty: A Kernel Embedding Approach

“…We also contribute over prior work [7] by circumventing the need for estimating the desired distribution in the distributon matching interpretation of CCO. To this end, we also extend [9] to reactive navigation in dynamic environments.…”

“…4: These figures illustrate how better favourable homotopy selection will lead to better distribution matching and hence, larger number of samples will be avoided don't assume any knowledge on the parametric form for the underlying distribution. We used a fixed set of 625 discrete control inputs to compute the one that led to the lowest value for the cost (9). We used γ = 0.1 in RBF kernel definition.…”

“…However, this requires reactive planners capable of operating under nonparametric uncertainty. To this end, we follow our prior work [7], [8], [9] which interprets CCO as a distribution matching problem. Specifically, we reformulate CCO as the problem of finding the appropriate control inputs that minimizes the deviation between the violation of velocity obstacle (VO) constraints and Dirac-Delta distributions.…”