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RANSAC stands for RANdom Sample Consensus. It is a relatively fast modeling technique for noisy data. 1. Picks random points form the data set 2. Creates a model 3. Finds outliners 4. Calculates an error 5. Then compares that error to the other models that have been created. Input • Data • Model to fit too • Min Number of points to generate a model • Min Tolerance for a model to be considered • Min number of inliers for model • Number of repetitions • Gait Frequency Output • Best Model • Best error • Best data set TERRAIN CHARACTERIZATION USING MODIFIED RANSAC ANALYSIS OF HUMAN GAIT DATA Christopher Sullivan, Elizabeth DeBartolo Ph.D., Kathleen Lamkin-Kennard Ph.D., Rochester Institute of Technology Department of Mechanical Engineering Rochester NY, USA About Foot Drop What: Foot Drop is only a symptom; it is the inability to dorsiflex the foot. Without dorsiflexion the foot can drag on the ground, which inevitably leads to tripping and over exertion of the hip and knee in attempts to compensate for the new height that the foot must reach to clear the ground. [1] Basics of the Gait Cycle Periods Initial Double- Limb Support Single-Limb Stance Second Double- Limb Support Initial Swing Mid- Swing Terminal Swing Foot Strike Opposite Toe-Off Opposite Foot Strike Toe-Off Foot Clearance Tibia Vertical Foot Strike Stance Swing % of Cycle 0% 62% 100% Gait Cycle With Foot Drop Periods Initial Swing Mid- Swing Terminal Swing Toe-Off Foot Crash Mid Trip Fallen Swing % of Cycle 62% 100% What is RANSAC? Noisy data set to be fit RANSAC fit with inliers in Blue and outliers in Red Research Goal: Current rigid Ankle-Foot Orthotics (AFOs) can be uncomfortable, but do allow people with foot drop to walk more normally. Many AFO users note that while descending stairs and ramps the natural tendency is to lead with the toe first, and most AFOs limit this kind of motion. With artificially limited plantar flexion, AFO users often feel extremely unstable on stairs and ramps. An ideal AFO would adjust for these terrain differences, but to do this the AFO must first know what kind of terrain it is walking over. The ankle mounted terrain detection presented here is capable of modeling five different ground types: level walking, and ascending or descending either stairs or ramps. The system is automated, and can be tailored to an individual because severity and complications that can be associated with foot drop cause individual user needs to vary widely. Eventually these models will be used with pattern recognition techniques to predict the type of ground the patient is walking over based on live, incoming data. Citations [1] Tina Taiming Chu PhD “Biomechanics of Ankle-Foot Orthoses: Past, Present, and Future” Volume 7, Number 4/Winter 2001 - Orthotic Management in Stroke [2] Silberstein, Nina. Foot Drop. [Online] November 2, 2008. http://www.ptproductsonline.com/issues/articles/2008-11_02.asp [3] Fischler, M. , & Bolles, R. (1981). Random sample consensus - a paradigm for model-fitting with applications to image-analysis and automated cartography. Communications of the ACM, 24(6), 381-395. Acknowledgments : This work was supported in part by the RIT Mechanical Engineering Department and an RIT&RGHS Seed Funding Award. User feedback was provided by Richard L. Barbano, MD (RGHS), PhD and J. J. Mowder-Tinney, PT, PhD and her clients at the Nazareth College Physical Therapy Clinic Test Equipment Infared Range Finder Selected Sharp GP2Y0A02Yk range between 8”-59” Summary of standardized Fourier coefficients Level Walking Descending Stairs Ascending Stairs Descending Ramp Ascending Ramp Mean SD Mean SD Mean SD Mean SD Mean SD a0 1.7314 0.036 1.7674 0.055 1.8820 0.049 1.7463 0.031 1.9250 0.003 a1 -0.4130 0.038 -0.8048 0.061 -0.6051 0.067 -0.5140 0.037 -0.3057 0.016 b1 0.1255 0.029 0.0605 0.069 0.1160 0.033 0.0940 0.039 -0.2228 0.001 a2 -0.0667 0.029 -0.2609 0.045 -0.3043 0.020 -0.0628 0.017 -0.0383 0.024 b2 -0.0573 0.017 0.0947 0.052 -0.0077 0.016 -0.0013 0.031 0.0441 0.026 a3 -0.1064 0.018 -0.0533 0.039 -0.0645 0.041 -0.1236 0.027 -0.1065 0.022 b3 -0.0821 0.014 -0.0447 0.026 0.0029 0.012 -0.0707 0.006 0.0768 0.003 a4 -0.0748 0.007 -0.0242 0.015 -0.0060 0.026 -0.0651 0.004 -0.0611 0.011 b4 0.0032 0.017 -0.0297 0.028 -0.0197 0.011 0.0385 0.015 -0.0158 0.005 w 4.6902 0.283 4.4016 0.324 4.2268 0.507 4.5173 0.573 4.9935 0.200 Results A comparison of the results show that the gait patters are statistically unique and that the process is not over fitting. This is important because for any pattern recognition to be feasible the patterns need to be statistically different from each other. Statistical uniqueness was determined by looking at the overlap of standard deviations on each Fourier coefficient. 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 Voltage (V) Time (sec) Standardized Level Walking 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 Voltage (V) Time (sec) Standardized Desending Stairs 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 Voltage (V) Time (sec) Standardized Assending Stairs 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 Voltage (V) Time (sec) Standardized Desending Ramp 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 Voltage (V) Time (sec) Standardized Assending Ramp 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 Voltage (V) Time (sec) Comparison of Standardization Level Stairs Down Stairs Up Ramp Down Ramp Up What follows is the result of averaging the time shifted Fourier coefficients from each test run to produce a standardized model of each situation Fourier series The model to be used in our RANSAC fitting process is a fourth order Fourier Series, which makes it trivial to scale the models to match the ever changing pace of the patient. 0 1 1 + 2 cos 2 + 2 sin 2 + 3 cos 3 + 3 sin 3 + 4 cos 4 + 4 sin 4 = 0 + 1 cos + 1 sin + cos 2 + si Improve the quality of life for people with Foot Drop by creating an Ankle-Foot Orthotic that can recognize and adapt to changing terrain. Jointed Brace Dynamic Walk Solid Brace Who: Foot Drop can affect individuals with neurodegenerative disorders, such as cerebral palsy, or stroke. It can also be affect individuals with Motor Neuron disorders, such as polio. Some people with foot drop have had some type of injury to the nerve roots of the leg. [2] Solutions: Ankle Foot Orthotics or AFOs are the current standard brace prescribed for people with foot drop. The illustration to the side represents the wide variety of shapes and functionalities that may be considered an AFO. Initial RANSAC fit to 7 level walking data sets. Curves do not coincide because data collection began at different points during the gait cycle. 0 0.5 1 1.5 2 2.5 0 5 10 15 20 25 Voltage (V) Time (sec) Original Inliers Fit 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 Voltage (V) Time (sec) 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 Voltage (V) Time (sec) 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 Voltage (V) Time (sec) Progression of Algorithm To show the progression of the data through the algorithm, level walking will be used as an example. This first plot shows the end result of RANSAC on a single data set. Only a small section of the data set is used to generate a Fourier series that is a very detailed representation of the rest of the data, without bias to noise. Each data set is time shifted so that the origin represent heel strike, using the angle sum identity: Each data set is then scaled by its period factor to account for pace variation. This gives a good representation of similarity between models IR Sensor attached to the leg

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