A number of useful mathematical tools have been applied to mobile robotics problems such as mapping, localization, navigation, perception, and so on. This seminar course will review three particularly applicable areas: linear algebra, probabilistic methods, and optimization techniques.



01/17 Linear algebra basics, Gaussian elimination, Gauss-Jordan elimination, inverses, LU decomposition, Crout's algorithm, rank, singular matrices Wes
01/19Vector properties, fundamental spaces of a matrix, eigen values and eigenvectorsWes
01/24Inverse existence/uniqueness, projections, solving inconsistent systems, bases, Gram-Schmidt orthogonalization, QR decomposition, pseudoinverses, SVD, properties of determinantsWes
01/26Eigenvalues and eigenvectors and their properties, matrix diagonalization, matrix exponentials, positive definite matricesWes
01/31Properties of probabilities and random variables, convolutions, least squares estimation, Normal random variables, central limit theorem, Markov inequality, Chebyshev inequality, weak law of large numbers, Jensen's inequality, Chernoff boundsKris
02/02General stochastic processes, Bernoulli process, Poisson process, random incidence paradox, Markov chainsKris
02/07Markov chains, Hidden Markov Models, Baum-Welch algorithm, Viterbi algorithm, training problemFlip
02/09Continuous HMM, null transition HMM, variable duration HMM, HMMs with sparse data, dynamic structure HMM, hybrid HMMFlip
02/14Markov decision processes (MDP), partial observability (POMDP), mobile robotics POMDP exampleFlip
02/16Monte Carlo integration, random number generation, variance reduction, antithetic variates, common random variates, control variatesKris
02/21Rao-Blackwellization, stratified sampling, importance samplingKris
03/07Importance sampling, sequential importance sampling, sequential Monte CarloKris
03/09Double session: Sequential Monte Carlo, bootstrap/particle filter, sampling distributions, resampling strategiesKris
04/06Markov-chain Monte Carlo, Metropolis-Hastings, MCMC convergence, Gibbs samplingKris
04/26Graphical models, belief propagation, loopy BP, nonparametric BPKris
03/14Spring break 
03/16Spring break 
03/23Nonlinear optimization basics, univariate minimizationFlip
03/28Steepest descent, convergence of steepest descent, conjugate gradient descentFlip
04/04Unconstrained optimization, random walk, pattern search, Powell's method, steepest descent, conjugate gradient, quasi-Newton methods, second-order methods, Wolfe's rule, Goldstein-PriceFlip
04/11Constrained linear programming, Simplex, constrained nonlinear programming, exterior penalty function method, augmented Lagrange multiplier methodFlip
04/13Simplex example, convergence rate, Levenberg-Marquardt, nonlinear least squaresFlip
04/18Direct constrained optimization, sequential linear programming, sequential quadratic programming, generalized reduced gradient, sequential gradient restorationFlip
04/13Lagrange multipliersWes
04/20Lagrange multipliers, quadratic programming with equality constraints, quadratic programming with inequality constraints, Karush-Kuhn-Tucker (KKT) conditionWes