Robotics Research by Antonio Bicchi & Wolfram Burgard

Author:Antonio Bicchi & Wolfram Burgard
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

5 Variance-Reduced Monte Carlo for Computing Pathwise CP

5.1 Control Variates

As discussed in Sect. 2.2, a good control variate h for f should have a known (or rapidly computable) expected value, and should be highly correlated with f. As mentioned in the previous section, existing probability-approximation methods, while not accurate in absolute terms, can act as very good proxies for CP in that they resemble a monotone function of the CP. Coupled with the fact that such approximations are extremely fast to compute, they make ideal candidates for h.

Fig. 3 a Approximation of an obstacle set as a union of half-planes. Half-planes for the dashed-line closest obstacle points are omitted, as their corresponding obstacle regions are occluded by a closer half-plane. The green ellipse represents the shape of the uncertainty covariance matrix which defines the “close” distance metric. b Comparison of MC variance-reduction methods applied to a path with true CP near 1%. Bands denote 95% confidence intervals for their respective estimates

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