Speed-independent vibration-based terrain classification for passenger vehicles

Transcription

1 Vehicle System Dynamics Vol. 47, No. 9, September 2009, Speed-independent vibration-based terrain classification for passenger vehicles Chris C. Ward and Karl Iagnemma* Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA (Received 21 November 2007; final version received 3 September 2008 ) Terrain physical characteristics can have a significant impact on passenger vehicle handling, ride quality, and stability. Here, an algorithm is presented to classify terrain using a single suspensionmounted accelerometer. The algorithm passes a measured acceleration signal through a dynamic vehicle model to estimate the terrain profile, and then extracts spatial frequency components of this estimated profile. A method is introduced to identify and remove terrain impulses from the profile that are caused by ruts and potholes. Finally, a supervised support vector machine is employed to classify profile segments as members of pre-defined classes (such as asphalt, brick, gravel, etc.). The classification algorithm is validated with experimental data collected with a passenger vehicle driving in real-world conditions. The algorithm is shown to classify multiple terrain types with reasonable accuracy at a range of typical automotive speeds. It is also shown that the removal of terrain impulses prior to classification improves classifier performance. Keywords: sensing; terrain; road roughness 1. Introduction and related work Terrain physical characteristics can have a significant impact on vehicle handling, ride quality, and stability. Terrain characteristics such as the friction coefficient (for on-road environments) and soil cohesion and internal friction angle (for off-road environments) dictate tyre traction properties, with implications for longitudinal and lateral wheel slip [1]. Additionally, terrain roughness modulates the normal force acting on a tyre, which in turn affects vehicle handling characteristics [2]. The ability to automatically classify terrain traversed by a vehicle would be useful in many scenarios, since it would allow the formation of estimates of various physical properties (i.e. friction, cohesion, internal friction angle, etc.). These estimates could then be used to bound the range of safe manoeuvres in an automated hazard avoidance algorithm. Estimates of terrain physical properties could also be used in automatic tuning of traction control systems, anti-lock braking systems, or active or semi-active suspension properties. *Corresponding author. kdi@mit.edu ISSN print/issn online 2009 Taylor & Francis DOI: /

2 1096 C.C. Ward and K. Iagnemma In this paper, a sensing algorithm is presented to classify terrain using a signal recognitionbased approach. The algorithm operates on data measured by a single suspension-mounted accelerometer. The algorithm relies on the observation that distinct terrain types often possess distinct characteristic geometries and bulk deformability properties, which give rise to unique, identifiable acceleration signatures during interaction with a rolling tyre. The authors have previously proposed a wheel acceleration-based terrain classification method for planetary exploration rovers [3,4]. This work was developed for low-speed (i.e cm s 1 ) systems with rigid metallic wheels, and demonstrated good performance in its intended application. Terrestrial passenger vehicles, however, experience a much broader range of velocities than planetary exploration rovers. Additionally, many of the high-frequency vibrations caused by the interaction of a rigid tyre with terrain material are damped by rubber pneumatic tyres. Thus, direct application of the methods of Brooks and coworker [3,4] to the passenger vehicle case would yield poor results. Other researchers have investigated acceleration-based terrain classification methods based on feedback from a vehicle-mounted inertial measurement unit (IMU), which are designed for terrestrial robots operating at speeds of 1 5 m s 1 [5,6]. These methods, however, do not consider the effect of vehicle speed on the measured vibration signature. Variation in vehicle speed (over a given terrain) modulates the frequency and amplitude of the measured wheel acceleration. (Note that the relationship between amplitude and speed is a function of the vehicle suspension characteristics and input frequency. This relationship is explored in Section of this paper.) Again, it is expected that the wide range of speeds experienced by a passenger vehicle during normal operation (and thus, the wide variation in vibration signature arising from a given terrain type) would likely introduce significant error in algorithms designed solely for low-speed operations. Visual terrain classification may also be possible [7]; however, changes in lighting and visibility conditions can lead to errors. Additionally, visual methods are limited to classifying surface materials, whereas tactile methods, such as those proposed in this work, will in general classify the underlying load-bearing surface. For example, a vibration-based approach could detect asphalt under a thin layer of sand, but a visual approach could not. The classification method presented in this paper explicitly considers both frequency and amplitude effects, resulting in an algorithm that can classify terrain at widely varying vehicle speeds. It also explicitly models the effects of tyre and suspension damping. The key idea of the algorithm is that measurable wheel accelerations are the product of an underlying terrain profile. By performing terrain classification on an estimate of this profile which is a spatial, rather than a temporal signal the classification problem is decoupled from vehicle speed and tyre and suspension deformation effects. Figure 1 shows a flowchart of the proposed algorithm. Wheel vertical acceleration is measured using a single wheel carrier-mounted accelerometer. The measured time-domain wheel acceleration is passed through an inverse model of the combined tyre and suspension dynamics (the inverse dynamics block of Figure 1) to estimate the road profile as a function of time, (y(t)). Next, the absolute value of the vehicle speed is integrated to estimate the vehicle displacement (x(t)), which is combined with the road profile to form an estimate of the terrain elevation as a function of displacement, (y(x)). A method is introduced to identify and remove terrain impulses from the profile that are caused by ruts and potholes, since the presence of ruts and potholes degrades classifier performance. The road profile is then segmented into instances of constant length and decomposed into spatial frequency principal components (Section 2.1.2). The principal components are scaled to have similar magnitudes across terrain types, and the first k principal components are used for classification in a support vector machine (SVM) classifier [8]. The SVM is a supervised classifier, meaning that it is trained offline with segments of hand-labelled training data corresponding to the terrain classes of

3 Vehicle System Dynamics 1097 Figure 1. Flowchart for speed-independent vibration-based terrain classification algorithm. interest. (Further details on classifier training is given in Section 2.3.) Online classification of the unknown terrain is performed in real time with the SVM by comparing transformed measured data with similarly transformed training data. This paper is organised as follows. In Section 2, a description of the proposed algorithm is given. This includes a description of methods for estimating the road profile from wheel acceleration data and calculating spatial frequency components in Section 2.1, a method for identifying and removing terrain impulses from the data in Section 2.2, and an approach for offline training and online implementation of the terrain classifier in Sections 2.3 and 2.4, respectively. In Section 3, the experimental platform is introduced, and experimental results are presented that demonstrate accurate classification of multiple terrain types during normal driving conditions. In Section 4, conclusions are drawn from this work and future work is suggested. 2. Algorithm description 2.1. Waveform representation Profile estimation The terrain surface profile is estimated via a standard quarter-car model of tyre-suspension dynamics [9], shown in Figure 2. The model consists of a sprung mass, m s, which is onequarter the mass of the vehicle body, and an unsprung mass, m us, which is the mass of a single wheel and attached suspension components. The road height under the tyre at time t is y road (t), and the rate of change of the road height, ẏ road (t), acts as a velocity input to the rim of the tyre.

4 1098 C.C. Ward and K. Iagnemma Figure 2. Diagram of quarter-car model. The rubber pneumatic tyre is modelled as a spring and a damper, K t, B t, between the road and the unsprung mass. The vehicle s suspension is modelled as an additional spring and damper, K s, B s, between the unsprung and sprung masses. Linear spring-damper models are used in this work; however, in general, a nonlinear spring damper could be used if such a model has been identified for a target suspension or tyre [10]. The vertical velocities of the unsprung and sprung masses are v u and v s, respectively. D u and D s are the spring compression distances. By summing the forces acting on each mass, a state-space model of the quarter-car dynamics can be obtained: v B s B s K s 0 0 s m s m s m s v s v u B s B s + B t K s K t v u B t Ḋ s = m us m us m us m us D s + m us ẏ road. (1) 0 Ḋ u D u From Equation (1), a transfer function relating the unsprung mass vertical velocity, v u,to the road input, ẏ road, can be obtained: v u (s) ẏ road (s) = m s B t s 3 + (m s K t + B s B t )s 2 + (B t K s + B s K t )s + K s K t m s m us s 4 + (m s B s + m s B t + m us B s )s 3 + (m s K s + m s K t + B s B t + m us K s + B 2 s B2 s m us/m s )s 2 + (B s K s + B s K t + B t K s B s K s m us /m s )s + K s K t. (2) Equation (2) relates wheel vertical velocity to changes in road elevation. However, wheel vertical acceleration can be more easily measured than wheel vertical velocity with low-cost sensors. It is trivial to find a relation between wheel acceleration and road input, as v u (s) ẏ road (s) = sv ( ) u(s) ẏ road (s) = s vu (s). (3) ẏ road (s) Figure 3 shows a Bode plot of this transfer function using parameters for an experimental test vehicle described in Section 3.1. The tyre and suspension act as a high-pass filter (from road

5 Vehicle System Dynamics 1099 Figure 3. Bode plot of Equation (3) describing ratio of unsprung mass acceleration to terrain profile velocity input. velocity to tyre acceleration), with road input frequencies above 50 rad s 1 (8 Hz) strongly affecting wheel accelerations. This is intuitive, since a constant road input would drive an unsprung mass at constant velocity, and thus the acceleration would be zero. The road input frequency is a function of both the characteristic wavelength of terrain features and the vehicle speed. Table 1 shows input frequencies corresponding to combinations of terrain characteristic wavelengths and two vehicle speeds representative of city/off-road and highway driving. The table also gives representative terrain feature-type examples for each wavelength, with type definitions derived from [11]. At typical automotive driving speeds, road input frequencies below 10 rad s 1 correspond to changes in gross slope and elevation, and do not contain significant information related to terrain feature type. Additionally, the quarter-car model assumes point contact between the tyre and terrain; however, a typical automotive tyre will exhibit a contact patch length on the order of 10 cm due to deformation of the rubber tyre carcass. This contact patch will provide additional damping of high-frequency, small-wavelength terrain inputs. Thus, the majority of useful terrain information will likely be contained between 10 and rad s 1 ( Hz) at typical vehicle speeds. Analysis of the model described in Equation (3) and the results in Table 1 provide insight into which terrain types are likely to be identifiable via an accelerometer mounted onto a vehicle Table 1. Terrain wavelengths corresponding to combinations of vehicle speed and road input frequency. Profile input frequency Vehicle speed Wavelength (m) Representative feature types 1 rad s 1 11ms 1 ( 25 mph) 69 Hills/slopes (0.16 Hz) 27 m s 1 ( 60 mph) 170 Hills/slopes 10 rad s 1 11ms 1 ( 25 mph) 6.9 Small hills/slopes (1.6 Hz) 27 m s 1 ( 60 mph) 17 Small hills/slopes 100 rad s 1 11ms 1 ( 25 mph) 0.69 Very coarse gravel (16 Hz) 27 m s 1 ( 60 mph) 1.7 Boulders, speed bumps rad s 1 11ms 1 ( 25 mph) Coarse gravel (160 Hz) 27 m s 1 ( 60 mph) 0.17 Very coarse gravel, cobblestone rad s 1 11ms 1 ( 25 mph) Very fine gravel ( Hz) 27 m s 1 ( 60 mph) Fine/medium gravel

6 1100 C.C. Ward and K. Iagnemma unsprung mass. In Figure 3, at low frequencies, the gain approaches zero, indicating a poor classification signal for very large wavelength features, such as hills. The high midrange gain indicates a strong signal for classifying terrains such as gravel. The gain at high frequency is reduced, but remains finite, indicating that classification of fine terrains is possible. In the presence of sensor noise, the lowered high-frequency gain results in reduced signal-tonoise ratio, potentially making differentiation of fine terrain types difficult (i.e. asphalt and pavement). The proposed classification algorithm takes as an input an estimate of the terrain profile derived from measured unsprung mass accelerations, rather than the road input frequency which is difficult to directly measure in most applications. To obtain an estimate of the terrain profile, the transfer function relating the unsprung mass acceleration to the profile height is first found as ( v u (s) y road (s) = v u(s) s ẏ road (s) ) ( ) = s 2 vu (s). (4) ẏ road (s) The desired transfer function relating the road profile to the unsprung mass acceleration is then found as the inverse of Equation (4): y road (s) v u (s) = 1 ( v u (s)/y road (s)) = 1 s 2 (v u (s)/ẏ road (s)). (5) Substituting Equation (2) into Equation (5) yields the desired model for estimating road profile from the measured vertical wheel acceleration: y road (s) v u (s) = m s m us s 4 + (m s B s + m s B t + m us B s )s 3 +(m s K s + m s K t + B s B t + m us K s + Bs 2 B2 s m us/m s )s 2 +(B s K s + B s K t + B t K s B s K s m us /m s )s + K s K t m s B t s 5 + (m s K t + B s B t )s 4 + (B t K s + B s K t )s 3 + K s K t s 2. (6) Figure 4 shows a Bode plot of Equation (6). The response is similar to a double integrator below 6 rad s 1 (1 Hz) and a single integrator above rad s 1 (160 Hz). Figure 4. Bode plot of Equation (6) describing ratio of profile height to wheel acceleration input.

7 Vehicle System Dynamics 1101 It should be noted that, in practice, typical accelerometers have near-constant measurement biases. These biases can be partially estimated and removed; however, any uncompensated accelerometer bias can cause large-profile estimate deviations, which would appear as terrain slopes. For classification, only profile features on a relatively small (i.e. centimetres) scale are desired. Large-scale features will thus be removed before classification is performed. To derive a road profile estimate, a discrete-time transformation of Equation (6) is applied to the measured acceleration using standard techniques, after first subtracting the acceleration due to gravity from the measurement. To remove large-scale elevation content and bias errors, a quadratic best fit is performed on a moving data window (a 1 s window has been used here) and subtracted from the estimated profile, leaving only the relatively high-frequency terrain profile information estimate, ỹ(t). The remaining low-frequency content is removed in the spatial domain, after impulses are filtered, as discussed in Section Large-scale terrain elevation removal could also be accomplished using a properly designed high-pass filter. Next, vehicle displacement is estimated from the measured vehicle speed as: x(t) = t 0 V(t) dt, (7) where V(t)is the vehicle longitudinal speed. Then, it is straightforward to restate the profile in spatial, rather than temporal, coordinates as ỹ(x). Two additional manipulations are required to produce a profile estimate suitable for classification. When the vehicle is stopped, unique accelerometer data are collected in the temporal domain, producing redundant data points, ỹ(x(t stopped )). These N redundant points are removed and assigned the mean value of the profile each time the vehicle stops, such that y(x(t stopped )) = 1 N t start t stop ỹ(x), (8) where y(x) is the profile estimated at constant temporal sampling frequency, minus the redundant data points. Finally, for the spatial frequency decomposition performed in Section 2.1.2, the profile must be sampled at a constant spatial frequency. The final profile estimate, y(x), is obtained by interpolating y(x) at constant spatial intervals, x. A piecewise cubic spline interpolation has been used here. The choice of x determines the maximum spatial frequency and will be discussed further in Section It should be noted that the profile estimate is not expected to exactly match the true road profile, but instead is a representation of the profile as seen by the vehicle. The quarter-car model assumes that the tyre undergoes point contact with the rigid terrain. As mentioned previously, a finite-sized contact patch exists due to the deformation of the tyre carcass. The tyre therefore filters some small-wavelength terrain features. These features are not measurable via a suspension-mounted accelerometer and thus will not be included in the profile estimate. Additionally, terrain is generally not perfectly rigid. For deformable terrain, the profile estimate will be a representation of the deformed terrain, and is thus a function of the vehicle ground pressure and terrain physical parameters Terrain spatial frequency analysis To analyse the terrain spatial frequency, the profile estimate is first decomposed into l short segments of length L, where L is chosen as a compromise between two competing requirements.

8 1102 C.C. Ward and K. Iagnemma First, L sets the classification resolution: a homogeneous terrain patch should be longer than L to be classified correctly, thus suggesting that a smaller value of L is desirable to increase resolution. L also dictates the resolution of spatial frequencies into which the signal can be decomposed with a Fourier transform, where ( )( ) f s 1 x f min = numpoints = = 1 x L L, (9) where x, which cancels in this equation, is the spatial spacing of the profile data points from Section A small value of f min is desired to extract the maximum information for classification. For this work, L was chosen as 4 m, which allows the classification of terrain patches on the order of one vehicle length and a spatial frequency resolution of 0.25 cycles min 1. The choice of x in Section is also determined by frequency domain considerations. The spatial sampling frequency is ( ) 1 f s =, (10) x and the Nyquist frequency is then f Nyquist = f ( ) s 1 2 =. (11) 2 x The Nyquist frequency is the highest spatial frequency that can be resolved from the profile data and therefore corresponds to the minimum feature size that can be distinguished from the terrain. x should generally be greater than or equal to the distance traversed by the vehicle in one temporal sampling interval while travelling at normal operating speeds. In this work, x was chosen as 0.02 m. To compute terrain spatial frequency characteristics, the spatial power spectral density (PSD) of each of the terrain profile segments is calculated using Welch s method [12]. The PSD is then log-scaled. The notation P fi,y j is used to represent the log-scaled power at frequency i of terrain profile segment j. The frequencies range from f min = 0tof max = f Nyquist. To reiterate, the frequency components are spatial frequency components of the estimated road profile in units of cycles m 1, which are independent of the vehicle speed. These frequency components will be utilised in the classification algorithm described in Sections 2.3 and Impulse detection and removal Some terrain features, such as potholes and railroad crossings, are not representative of the underlying terrain type. Therefore, a method was developed to detect and remove impulses from the profile estimate before performing classification. The proposed impulse detection method is based on the hypothesis that the variation in a road profile should be relatively constant over a given terrain type. An impulse in the terrain will create a sharp, brief increase in profile variation. The following algorithm has been developed to identify impulses, with values adopted for this work given in parentheses: (1) Calculate the standard deviation of the road height over a short moving window (1 m). (2) Calculate the moving average of the standard deviation calculated above, over a longer window (16 m). (3) Check if the short-scale standard deviation calculated in (1) is greater than a specified multiple (3 ) of the large-scale average calculated in (2). If it is larger, label the point as an impulse.

9 Vehicle System Dynamics 1103 (4) For each detected impulse, grow the impulse back by a set distance (0.2 m). This compensates for the delay in detection of impulses, which is caused by the data being calculated over a window, and the requirement that the impulse must exceed a threshold before it is detected. Figure 5 shows an example of impulse detection from experimental data. The top plot shows the standard deviation values calculated in steps 1 and 2, while the bottom plot indicates the locations of detected impulses. Analysis of video captured during collection of this and other data has shown that impulses are correctly identified when the vehicle encounters sharp bumps or depressions in the terrain. It should be noted that this impulse detection scheme may label transitions from relatively smooth to rough terrains as an impulse; however, the impulse will be only detected briefly at the initial terrain transition while the moving average in step (2) adjusts to the new terrain type. The window size in step (2) adjusts how sharp an impulse must be to be detected and how quickly the method adjusts to changes in terrain type. After impulses are detected, they are removed from the data used for classification. Figure 6 illustrates the impulse removal process. The process begins with a terrain height vector, y(k), estimated using the procedure of Section 2.1.1, where k is the vector index at uniformly spaced displacements, x(k). Impulses are identified as described above, with a given impulse having impulse start index k is and impulse end index k ie. The impulse is removed (Figure 6c) by eliminating y(k is + 1) through y(k ie + 1) to form the truncated profile vector y t, where y t =[, y(k 2 ), y(k 1 ), y(k is ), y(k 1 ), y(k 2 ), ]. (12) Finally, the profile estimate is adjusted to be zeroth-order continuous (Figure 6d). The adjusted and truncated profile vector, y at, is calculated as y at (k) = { y t (k), k k is, y t (k) + (y(k is ) y(k ie )), k >k is. (13) Figure 5. Example of impulse detection.

10 1104 C.C. Ward and K. Iagnemma Figure 6. Illustration of impulse removal process. The above procedure is repeated to remove all detected impulses from the profile vector before classification. For notational convenience, the profile vector in the following sections will be referred to as y, without the double prime notation. Unless otherwise noted, it is assumed in future sections that impulses have been removed from the profile estimate vector such that y = y at A priori classifier training The purpose of a priori training is to teach a classifier to recognise profile signatures of distinct terrain types of interest. Training data are collected by manually driving the instrumented vehicle over known terrain types and recording the corresponding vibration signatures. In theory, the driving speed for training data can be arbitrary; however, in practice, improved results are likely to be achieved by collecting data at a range of expected driving speeds, due to unmodelled nonlinearities in the vehicle suspension. The training data for this work were collected during normal driving at variable speeds, which did not necessarily correspond to testing data driving speeds. Data are collected using a single-axis accelerometer mounted onto the vehicle suspension with its measurement axis aligned with the direction of suspension travel. Training data are converted from unsprung mass vertical accelerations to a profile estimate (Section 2.1.1), impulses are removed (Section 2.2), and the profile is decomposed into segments which are represented as spatial frequency components (Section 2.1.2). For training, the profile is broken into l non-overlapping segments such that all data are only used once. The frequency components of each terrain segment are then formed in a matrix, Y, as P fmin,y 1 P fmin,y l Y = (14) P fmax,y 1 P fmax,y l In this form, each column of Y contains the frequency components of a single terrain segment. To reduce dimensionality, principal component analysis is used to form a smaller set

11 Vehicle System Dynamics 1105 of components for classification. First the rows of Y are mean-adjusted to form the matrix Ŷ: mean(p fmin ) Ŷ = Y. [ 1 1 ]. (15) mean(p fmax ) Singular value decomposition [3,13] is then used to separate Ŷ into three matrices, U a, S a, and V a, such that Ŷ = U a S a V T a, (16) where U a is a unitary matrix with the principal components of Ŷ as columns, S a a diagonal matrix of singular values, and V a a unitary matrix with the principal components of Ŷ T as columns. For dimensionality reduction, only the principal components that explain a majority of the signal variation are retained. To compute the first n principal components, first the matrix U signal is formed from the first n columns of U a, and S signal is formed from the upper-left n n block of S a. Choosing too high a value for n can result in overtraining the classifier to recognise noise in the training data, and decrease performance when classifying new data [3]. For this work, the first 10 principal components have been used (n = 10). Finally, the principal components of the terrain profile spatial frequency content are calculated as W training = S 1 signal UT signaly. (17) W training is the feature-instance matrix used in the offline training phase for terrain classification, where each of l instances is described by n principal component features. W training is an n l matrix of the form W training = PC 1,y1 PC 1,yl PC n,y1 PC n,yl. (18) Here an SVM classifier is used to determine class boundaries within the n-dimensional feature space [14]. Each distinct terrain type is assigned a unique positive integer label, and an l 1 training label vector, c =[c 1 c l ] T, is formed using the known terrain labels for the training data [8,15]. In this work, each instance was manually labelled with a terrain class based upon a video record of the driving data. Classification accuracy is improved by scaling each feature type to have similar magnitudes [8]. To scale each feature to the range [ 1, 1], the n n scale factor matrix, S, is formed such that { 1 S i,j = max( column j of, if i = j, W training ) (19) 0, otherwise, and the scaled training feature matrix, W training, is then W training = W training S. (20) W training and c are used to train an SVM using a radial basis function (RBF) kernel. An RBF kernel was chosen because it performs well with both nonlinear and linear class relations and requires few kernel parameters [8]. SVM parameters are determined using a grid search to systematically find a parameter set that minimises the average classification error and error

12 1106 C.C. Ward and K. Iagnemma standard deviation of a v-fold cross-validation [8]. The final SVM model is trained using the best SVM parameter set and the entire training data set. The parameter search and SVM training can be computationally expensive. However, training is performed only once, offline, producing an SVM model suitable for computationally inexpensive online classification. The principal component vectors (defined by S 1 signal UT signal ), feature scale factor matrix, S, and trained SVM model are retained for online classification Online classification During online classification, wheel accelerometer data are collected at the same rate as for training data collection. Accelerometer data are converted to a profile estimate and impulses are removed. For this work, terrain is classified each time the vehicle travels over a unique terrain patch of length L. In practice, the classified terrain patches can overlap for increased terrain transition detection resolution and speed, with the degree of overlap limited by available computation. For each profile segment, the PSD is calculated, and the log-scaled elements are placed in the vector: y test = P fmin,y test. P fmax,y test. (21) The principal components obtained for the training data are calculated for the online segment using the same transformation matrices, S signal and U signal : W test = S 1 signal UT signal y test, (22) W test = PC 1,ytest. PC n,ytest and the features are scaled using the retained feature scaling matrix, S:, (23) W test = W test S. (24) At each data instance, terrain is classified using the SVM model generated in the offline classification and the scaled test feature vector, W test. The SVM outputs estimates of the terrain class label and probability that the label is correct [5]. To improve classification accuracy at the expense of labelling all data, instances with a probability estimate below a set threshold level (chosen at 65% for this work) can be labelled as unknown. Instances labelled as unknown are caused by traversing terrain which the algorithm was not trained to recognise or terrain whose vibration signature does not closely match the training data. 3. Experimental results 3.1. Experimental platform A standard coupe-style passenger vehicle, a 1994 BMW 325is, has been instrumented to experimentally validate the terrain classification algorithm presented in this work (Figure 7). Approximate quarter-car model parameters have been identified for this vehicle and are listed

13 Vehicle System Dynamics 1107 Figure 7. Experimental vehicle. in Table 2. An Analog Devices ADXL320 dual-axis accelerometer has been mounted on the suspension as shown in Figure 8, with one axis aligned with the vertical suspension travel. The accelerometer has a dynamic range of ±49ms 2 and is low-pass filtered at 250 Hz, yielding 0.05 m s 2 resolution. The accelerometer is sampled at 512 Hz using a PC104-based data logging system equipped with a Diamond Systems Diamond-MM-32-AT data acquisition board with a 16-bit A/D resolution. The electronics package (Figure 9) is also equipped with a Novatel ProPak-G2plus GPS receiver used to measure vehicle speed with a sample rate of Table 2. Quarter-car model parameters used for experimental vehicle. Parameter m s m us K s K t B s B t Value 325 kg 32.5 kg kn m kn m kg s 1 50 kg s 1 Figure 8. Accelerometer mounting location on experimental vehicle suspension.

14 1108 C.C. Ward and K. Iagnemma Figure 9. Experimental electronics package. 8 Hz and a Crossbow AHRS400 IMU to measure vehicle tilt and acceleration with a sample rate of 512 Hz. The GPS receiver has an advertised velocity accuracy of 0.3 m s 1 RMS. The IMU-based vehicle acceleration measurements were used in a Kalman filter with a 1-DOF kinematic model to augment the GPS velocity measurements between samples and during periods of poor GPS reception Results The experimental vehicle was driven over 12 km in normal driving conditions near Middlesex Fells, Massachusetts, in fair weather. The driving was on public roads and included many turns, starts, and stops. The vehicle was driven over a variety of asphalt road surfaces including highways, town roads, rough parking lots, and numerous potholes. Additionally, the vehicle was driven on a brick road, a gravel parking lot, a highway rumble strip, and a grass shoulder. Figure 10 shows images of the brick, gravel, and grass terrain types, with a screwdriver shown in the picture for scale. Table 3 shows the number of 4 m instances of each terrain type used for training and testing the classifier algorithm. Due to the small amount of grass data available, the classifier was not trained to detect grass. The grass data were included when testing the algorithm to give an example of how the classification algorithm treats an untrained terrain type. In general, training data should be representative of variations in the given terrain class and a similar number of training instances should be selected for each class. The relative number of training instances was not optimised in this work. The vehicle was driven at speeds ranging from 0 to 104 km h 1 (0 29 m s 1 ). The training data had a (spatial) mean vehicle speed of 41 km h 1 (11.4 m s 1 ) and median of 21 km h 1 (5.8 m s 1 ), while the testing data had a (spatial) mean speed of 57 km h 1 (15.8 m s 1 ) and a median of 55 km h 1 (15.3 m s 1 ). Both training and testing data were hand-labelled with the true terrain type. Small errors in the hand labelling are possible, and thus perfect classification accuracy would not be expected. The proposed classification algorithm was trained on the 2 km of the training data and then tested on the remaining 10 km of the testing data. Table 4 shows the classification results by the terrain class, with data classified with <65% confidence labelled as unknown.

15 Vehicle System Dynamics 1109 Figure 10. Table 3. Photos of brick, gravel, and grass terrains. Number of 4 m long training and testing instances by terrain type. Terrain type Training instances Testing instances Asphalt Brick Gravel Rumble strip Grass 0 7 Total instances Total distance (km) Table 4. Classification results using the proposed algorithm with 65% threshold. Actual label Asphalt (%) Brick (%) Gravel (%) Rumble Strip (%) Grass (%) Classified as Asphalt Brick Gravel Rumble strip Unknown Note: Note that classifier is not trained to recognise grass. For all terrain types, the majority of data was either labelled correctly or as unknown : 89.2% of the data instances were labelled correctly, 8.4% were labelled unknown, and only 2.4% were labelled incorrectly. Of the labelled data, 97.4% was labelled correctly. This suggests that, rather than return an incorrect class label, the algorithm tends to assign an unknown label to questionable data instances. Additionally, the majority of the grass data was labelled as unknown, indicating that the algorithm is relatively robust to untrained terrain types. Increasing

16 1110 C.C. Ward and K. Iagnemma the confidence threshold would reduce incorrectly labelled instances by labelling additional instances as unknown. The tradeoff between classification accuracy and completeness can be chosen based upon application requirements. Overall, the classification results are good, particularly considering that with the exception of the grass, each terrain type is a hard surface and might be expected to give a similar vibration signature. The large variety of asphalt surfaces used for training the classifier in this work allows the algorithm to correctly identify many terrain variations as asphalt. However, using such a broad class type definition may result in low classifier confidence when distinguishing similar terrains, such as rough asphalt and gravel, which may overlap in some portions of the classifier principal component space. In this work, the confidence threshold was selected such that these terrains would tend to be labelled as unknown. Figure 11 shows a 2.5 km subset of the 10 km of test results. The top plot shows the vehicle speed, the middle plot the actual and predicted terrain types, and the bottom plot the probability estimate. For readability, the terrain types in the middle plot have been decimated by a factor of 3. Figure 12 shows the classification accuracy versus vehicle speed. The figure shows both the percentage of correctly classified instances out of all instances in the speed range and the percentage of correctly classified instances out of the classified instances. Over all speed ranges, over 89.5% of the labelled data were labelled correctly. The slightly lower accuracy at a low speed is likely due to the increased amount of non-asphalt data at lower speeds. Some algorithm tuning is possible with the choice of SVM parameters. For the results presented above, an SVM cross-validation was performed to maximise the classification accuracy for all terrain classes, giving equal weight to each class. An alternative metric is to choose parameters resulting in the highest total accuracy. Using such a metric, 90.2% of the data were classified correctly, a small improvement over the 89.3% accuracy given above. However, as shown in Table 5, because more asphalt data were available than other terrain types, this metric has the effect of overtraining the classifier to detect asphalt and results in a decreased classification accuracy for the other terrain types. Table 6 and Figure 13 show the classification results using the terrain classification algorithm without filtering impulses from the data before classification. The classified accuracy is actually Figure 11. Subset of terrain classification results using the proposed algorithm. Percentage accuracies are for the entire 10 km test set. Note that classifier is not trained to recognise grass.

17 Vehicle System Dynamics 1111 Figure 12. Terrain classification results versus speed using enhanced algorithm. Dotted lines show average accuracy over all speeds. Table 5. Classification results using enhanced algorithm with SVM parameters chosen to provide maximum combined accuracy. Actual label Asphalt (%) Brick (%) Gravel (%) Rumble strip (%) Grass (%) Classified as Asphalt Brick Gravel Rumble strip Unknown Note: Note overtraining for asphalt classification at expense of accuracy on other terrains. Table 6. Classification results using enhanced algorithm without removing impulses. Actual label Asphalt (%) Brick (%) Gravel (%) Rumble strip (%) Grass (%) Classified as Asphalt Brick Gravel Rumble strip Unknown increased to 98.4%, from 97.3%; however, this is at the expense of more data being labelled unknown. The algorithm appears to assign an unknown class to the majority of instances containing impulses. However, it should be noted that there are two significant benefits to impulse removal. First, detecting the presence of an impulse provides more information than labelling the instance containing the impulse as unknown. Secondly, an impulse is generally shorter than the 4 m terrain segments. If labelled as an impulse, only the data containing the impulse are removed; however, if labelled as unknown, the entire 4 m segment is unclassified.

18 1112 C.C. Ward and K. Iagnemma Figure 13. Subset of terrain classification results using enhanced algorithm without removing impulses. 4. Summary and conclusions An algorithm has been presented for the vibration-based terrain classification for passenger vehicles. The algorithm creates an estimate of the terrain profile from measured wheel accelerations. Spatial (rather than temporal) frequency components of the estimated profile are used as speed-independent features for classification. Good algorithm performance has been experimentally demonstrated during testing on multiple terrain types at a wide range of vehicle speeds. In addition to the terrain estimation algorithm, a technique for detecting terrain impulses has been developed, which can accurately detect terrain features such as potholes. Future work should investigate algorithm sensitivity to varied vehicle parameters. Variations in vehicle mass are expected due to cargo and passenger changes, and robustness to these variations should be investigated. Robustness to changes in tyre pressure and suspension ageing should be investigated as well. Also of interest is testing classifier performance with an increased number of terrain types and more precise groupings of terrain-type classes (such as splitting the asphalt class into several roughness groupings). References [1] K. Iagnemma, S. Kang, H. Shibly, and S. Dubowsky, Online terrain parameter estimation for wheeled mobile robots with application to planetary rovers, IEEE Trans. Robot. 20(5) (2004), pp [2] M. Blank and D. Margolis, The effect of normal force variation on the lateral dynamics of automobiles, Paper No , Society of Automotive Engineers, [3] C. Brooks, Terrain identification methods for planetary exploration rovers, Master s thesis, Massachusetts Institute of Technology, [4] C. Brooks and K. Iagnemma, Vibration-based terrain classification for planetary exploration rovers, IEEE Trans. Robot. 21(6) (2005), pp [5] E. DuPont, R. Roberts, C. Moore, M. Selekwa, and E. Collins, Online terrain classification for mobile robots, Proceedings of IMECE 2005, Orlando, USA, [6] L. Ojeda, J. Borenstein, G. Witus, and R. Karlsen, Terrain characterization and classification with a mobile robot, J. Field Robot. 23(2) (2006), pp [7] R. Manduchi, Learning outdoor color classification, IEEE Trans. Pattern Anal. Mach. Intell. 28(11) (2006), pp [8] C.-W. Hsu, C.-C. Chang, and C.-J. Lin, A practical guide to support vector classification, Available at cjlin/papers/guide/guide.pdf (Accessed August 2006).

19 Vehicle System Dynamics 1113 [9] J.Y. Wong, Theory of Ground Vehicles, 3rd ed., Ch. 1, John Wiley & Sons, New York, NY, [10] J. Rauh and M. Mössner-Beigel, Tire simulation challenges, IAVSD 2007, Prague, Paper 104, Taylor & Francis. [11] Particle size, Wikipedia, the Free Encyclopedia. Available at (Accessed 20 March 2007). [12] P.D. Welch, The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms, IEEE Trans. Audio Electroacoust. AU-15 (1967), pp [13] G.H. Golub and C.F. Van Loan, The Singular Value Decomposition and Unitary Matrices, Matrix Computations, 3rd ed., Johns Hopkins University Press, Baltimore, MD, [14] C.-C. Chang and C.-J. Lin, LIBSVM: a library for support vector machines, Available at cjlin/libsvm. [15] T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer, New York, 2001.