gMapping - Advanced Robotics - Lecture Slides, Slides of Robotics

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gMapping

n gMapping is probably most used SLAM algorithm n Implementation available on openslam.org (which has many more resources) n Currently the standard algorithm on the PR

gMapping Overview

n Rao-Blackwellized Particle Filter n Each particle = sample of history of robot poses + posterior over maps given the sample pose history; approximate posterior over maps by distribution with all probability mass on the most likely map whenever posterior is needed n Proposal distribution ¼ n Approximate the optimal sequential proposal distribution p(xt) = p(xt | x i 1:t-1,^ z1:t, u1:t) / p(zt | m i t-1,^ xt ) p(xt |^ x i t-1,^ ut)^ [note integral over all maps^ à^ most likely map only] n 1. find the local optimum argmaxx p(x) n 2. sample xk^ around the local optimum, with weights wk^ = p(xk) n 3. fit a Gaussian over the weighted samples n 4. this Gaussian is an approximation of the optimal sequential proposal p n Sample from (approximately) optimal sequential proposal n Weight update for optimal sequential proposal is p(zt | x i 1:t-1,^ z1:t-1,^ u1:t) = p(zt | mi t- , xi t- , u t- ), which is efficiently approximated from the same samples as above by n Resampling based on the effective sample size Seff

Key Ideas

n Find argmax x_t p(z t | m i t- , x t ) p(x t | x i t- , u t

n p(x t | x i t- , u t ) : Gaussian approximation of motion model, see previous slide n p(z t | m i t- , x t ) : “any scan-matching technique […] can be used” n Used by gMapping: “beam endpoint model” = likelihood field More on scan-matching in separate set of slides

Scan-Matching

n “Most maps generated can be magnified up to a resolution of 1cm without observing considerable inconsistencies” n “Even in big real world datasets covering […] 250m by 250m, [..] never required more than 80 particles to build accurate maps.” Correctness evaluated through visual inspection by non-authors

Experiments