Presented by: Rafael O. Batista Jorge Wall Following Robot Path Planning Problem: A Statistical Learning Approach Universidad de Puerto Rico Recinto Universitario de Mayagüez ININ6048 Final Project Presentation Mayagüez, 2016

Agenda  Problem overview  Dataset description  Methods  Preprocessing  Selected machine learning algorithms  Performance measures  Stacked learner  Results  Preprocessing  Selected machine learning algorithms  Performance measures  Stacked learner  PCA vs LDA  Conclusions

Problem overview  Automatic robot path planning decision  Multiple type of applications  Learning from environment (Sensor measurements)  Different types of approaches o Heuristic approaches (Fuzzy logic) o Geometric base approaches (Optimization based map search) o Machine learning algorithms (Supervised and unsupervised)  Open research problem o Real time execution o Dynamic environments o Unknown environments Image by Simeon87, distributed under a CC-BY 2.0 license.CC-BY 2.0 license

Problem overview  SCITOS G5 robot Photograph by MetraLabs.

Dataset description VariableDescriptionTypeValuesPredictorMissing Values UDS1 Position Angle = 180º Quantitative (0.400,0.401,0.402), (5.000,4.866, 4.860) YES0% UDS3Position Angle = -150º Quantitative (0.470,0.471,0.492), (5.029,5.028, 5.026) YES0% UDS6Position Angle = -105º Quantitative (1.114,1.115,1.118), (5.005,5.000, 4.980) YES0% UDS9Position Angle = -60º Quantitative (0.836,0.854,0.861), (5.000,4.956, 4.955) YES0% UDS12Position Angle = -15º Quantitative (0.778,0.779,0.780), (5.000,4.992, 4.981) YES0% UDS15Position Angle = 30º Quantitative (0.495,0.496,0.497), (5.000,4.921, 4.920) YES0% UDS18Position Angle = 75º Quantitative (0.354,0.355,0.356), (5.000,4.608, 4.591) YES0% UDS21Position Angle = 120º Quantitative (0.380,0.381,0.382), (5.000,4.822, 4.812) YES0% UDS24Position Angle = 165º Quantitative (0.377,0.380,0.381), (5.000,4.871, 4.865) YES0% Move ForwardPath Following Decision Qualitative 2205 (44.41%)NO0% Sharp Right TurnPath Following Decision Qualitative 2097 (38.43%)NO0% Slight Left TurnPath Following Decision Qualitative 328 (6.01%)NO0% Slight Right TurnPath Following DecisionQualitative826 (15.13%)NO0%  Twenty four sensors (Quantitative)  Four classes

Methods  Preprocessing  Multivariate normality test  Henze-Zirkler’s Multivariate Normality Test  Mardia’s Mutivariate Normality Test  Chi square Q-Q plot  Outlier detection  Mahalanobis distance (Assumes MVN dataset)  Random forest instance proximity (No normality assumption)  Collinearity and dimensionality reduction  Principal components analysis o Correlation matrix (scaling) o Explained variance (number of principal components) o Unsupervised  Linear discriminant analysis o Assumes normality o Class separation o Supervised

Methods  Selected machine learning algorithms ?  Random forest  Non parametric and supervised  Ensemble (Bagging)  k-NN  Non parametric  Supervised

Methods  Selected machine learning algorithms  Support Vector Machine  Cost  Gamma  Kernel Trick  Non linear  Different types of kernel: o Linear o Polinomial o Radial

 Selected machine learning algorithms Methods  Support Vector Machine Cost = 100Cost = 0.1

 Performance measures  Classification error  Kappa statistics  Multiclass Logarithmic Loss Methods  Desirability Function

 Selected machine learning algorithms Methods  Stacked learner Prob. KNN Neighbors = 9 Prob. RF N.Trees = 100 Prob. SVM Degree = 3 Dataset Class Labels PCA Rotated Dataset CV RF Result

Results  Preprocessing: Multivariate normality test.

Results  Preprocessing: Outlier detection

Results  Preprocessing: PCA Scree plot and explained variance PC1PC2PC3PC4PC5PC6PC7PC8PC9PC10PC11PC12PC13PC14PC15 Standard deviation Proportion of Variance Cumulative Proportion

Results  Preprocessing: LDA Histogram First linear discriminant loading’s histogram.

Results  Preprocessing: LDA Histogram Second linear discriminant loading’s histogram.

Results  Preprocessing: LDA Histogram Third linear discriminant loading’s histogram.

Results  Tuning: RF LDA loadings dataset tuning

Results  Tuning: RF PCA rotated dataset tuning

Results  Tuning: SVM with LDA loadings dataset (radial kernel)

Results  Tuning: SVM with PCA rotated dataset (polynomial kernel)

Results  Tuning: SVM with PCA rotated dataset (polynomial kernel)

Results  Tuning: Summary table for SVM DatasetKernelDegreeCostGamma Resulting Error PCA rotated RadialNA PCA rotated PolynomialThird LDA loadings RadialNA

Results  Implementation: PCA rotated dataset and kNN

Results  Implementation: PCA rotated dataset and RF

Results  Implementation: PCA rotated dataset and SVM

Results  Implementation: Dataset for stacked approach

Results  Implementation: PCA rotated dataset stacked learner

Results  Implementation: LDA loadings dataset and kNN

Results  Implementation: LDA loadings dataset and RF

Results  Implementation: LDA loadings dataset and SVM

Results  Implementation: LDA loadings dataset and stacked learner PCA

PCA vs LDA  Comparing kNN performance PCA LDA

PCA vs LDA  Comparing RF performance PCA LDA

Conclusiones  The best performance of our proposal was obtained by using RF and the LDA loadings dataset, with a desirability value of 94.75%.  The stacking approach was successfull, and improved the desirability value to 99.99% for both cases, LDA and PCA.  Machine learning techniques are useful for this kind of path planning problems with dynamical or unknow enviroments.  Future work may considered the use of better optimization strategies for the selection of optimal parameter for SVM.

References Fletcher, T. (2009). Support Vector Machines Explained. Retrieved from Freire, A. Veloso, M. Barreto, G. (2010). UCI Machine Learning Repository [ Irvince, CA: University of California, School of Information and Computer Science. Freire, A. L., Barreto, G. A., Veloso, M., & Varela, A. T. (2009). Short-term memory mechanisms in neural network learning of robot navigation tasks: A case study th Latin American Robotics Symposium, LARS 2009, (4). Hastie, T. J., Tibshirani, R. J., & Friedman, J. H. (2009). The elements of statistical learning: data mining, inference, and prediction. book, New York: Springer. MetraLabs GmbH. (2011). SCITOS G5 Embedded PC and Operating System. Retrieved December 14, 2016, from Otte, M. W. (2015). A Survey of Machine Learning Approaches to Robotic Path-Planning. Cs.Colorado.Edu. Retrieved from Modeling Prelim/Otte.pdf