State-Space Systems Open-loop Estimators Closed-loop Estimators Observer Theory (no noise)-Luenberger IEEE TAC Vol 16, No. 6, pp. 596-602, December 1971 Estimation Theory(with noise)-Kalman Copyright [2001 by JOnathan dHow

Closed-loop system analysis Robustness State-space -eigenvalue analysis Frequency domain- Nyquist theorem Sensitivity Copyright 2001 by Jonathan How

MIMO Systems Singular Value Decomposition Multivariable Frequency Response Plots Copyright 2001 by Jonathan How

Bounded gain There exist very easy ways of testing(analytically) whether S Gu)< SISO Bounded Gain Theorem: Gain of generic stable system

Weighting Matrix Selection a good rule of thumb when selecting the weighting matrices Rxx (or Ru and R uu is to normalize

Partially Observable Markov Decision Processes Part II Additional reading: Anthony R. Cassandra. Exact and Approximate Algorithms for Partially Observable Markov Decision Processes. Ph. D. Thesis. Brown University Department of Computer Science, Providence, RI

Review: Constraint-based Interval Planning Simple Temporal Networks Schedulability and Scheduling Review: Temporal, Model-based Programming Managing Execution Uncertainty Execution with Dynamic Scheduling Execution with Explicit Models of Uncertainty

Defining problem and model so| ution: Minimizing localization error Comb imize gain in explored map bined Information Utilities Integrated Adaptive Information-based Exploration Algorithm

Outline Lightning Summary Black Box Model of SIFT SLAM Vision System Challenges in Computer Vision What these challenges mean for visual SLAM How SIFT extracts candidate landmarks How landmarks are tracked in SIFT SLAM Alternative vision-based SLAM systems Open questions

Vision-based SLAM Mobile Robot Localization And Mapping With Uncertainty using Scale-Invariant Visual Landmarks -e,lowe, Little Vikash Mansinghka Spren Riisgaard Outline