Model-based fault detection and isolation for a powered wheelchair

This paper presents a model-based fault detection and isolation (FDI) for a powered wheelchair handling faults of both the internal sensors (two wheel-resolvers and a gyro) and the external sensor (a forward-looking laser range sensor), as well as actuators (two wheel motors). Hard faults of the internal sensors and actuators are diagnosed based on mode probability estimated with interacting multi-model estimator. Soft faults, which appear in the internal sensors as change of sensor gains, are diagnosed based on estimating the robot velocity with the fault-free external sensor via scan matching method. Faults of the external sensor are detected based on errors related to the scan matching. Experimental results in indoor environments show the performance of our FDI method.

In our previous paper, we presented model-based FDI for mobile robots and powered wheelchairs (Hashimoto et al., 2001;; external sensors and actuators were assumed to be always fault free, and only the faults of internal sensors were handled. The IMM estimator and Kalman filter were applied to FDI of the internal sensors. In this chapter, we present model-based FDI for a powered wheelchair handling faults of both the internal and external sensors, as well as actuators. This chapter is organized as follows: Section 2 overviews our experimental wheelchair. Sections 3 and 4 present the FDI method for internal sensors and actuators, and Section 5 presents the FDI method for external sensors. In Section 6, we describe experiments conducted in a typical indoor environment to evaluate the FDI method, followed by our conclusions. Figure 1 shows the powered wheelchair used in the experiments; it has wheel units on the left and right sides to achieve differential steering. The wheel units each consist of a wheel motor and a wheel resolver. The wheel resolver measures the wheel velocity. A yaw-rate gyro is attached to the chassis of the wheelchair to sense the turn velocity. A laser range sensor (LRS) is mounted at the front side of the wheelchair to sense environments. It takes a laser scan image, which is represented by a sequence of distance samples in the horizontal half plain. The angular resolution of the LRS is 0.5 [deg], and one scan image contains 361 distance samples. We handle the faults of three internal sensors (two wheel resolvers and one gyro), one external sensor (LRS) and two wheel motors.

Internal Sensor FDI
First, we consider the hard faults of the wheel resolver and the gyro-the sensor fails completely, and the sensor output is stuck at a constant value. A dynamic model related to the left and right wheel units is derived by Laser where i = left (wheel) and right (wheel). v i is the wheel velocity and Δv i is the disturbance. u i is the input of the wheel unit. A i and B i are constants. We assume that the wheelchair moves stably at an almost constant velocity through faulttolerant operation, even though sensor faults have occurred. The dynamic model related to the turning motion of the wheelchair is then assumed to be where   is the turning velocity and    is the disturbance.
When the sensor output of the hard fault is assumed to be stuck at zero, the measurement model related to the wheel unit is Hard fault model (m 1 ): where z i is the output of the wheel resolver. Δz i0 and Δz i1 are the sensor noises. Because the wheel resolver is assumed to be stuck at zero on the hard fault, the measurement is modeled by zeroing out the kinematic function, as in Eq. (4). If it is stuck at a nonzero value on the hard fault, the measurement is modeled by The gyro output is also modeled by Fault-free model (m 0 ): z gyro (t) =   (t) + Δz gyro0 (t) Hard fault model (m 1 ): z gyro (t) = 0 + Δz gyro1 (t) We assume that the disturbances and the sensor noises are both zero means and white Gaussian sequences, and we estimate the mode probability based on Eqs.
(1)-(6) via the IMM estimator (Zhang & Li, 1998;Hashimoto et al., 2001). The mode probability provides an indication of FDI of the internal sensor; for example, we consider FDI of the gyro and denote the mode probability estimates of fault free and hard fault by  0 and   , respectively. The fault decision is made based on simple logic: If  0 >   , then the gyro is fault free; else, a hard fault occurs. The stop condition of the wheelchair results in wheel resolver FDI making an incorrect fault decision, because it makes the sensor output zero. In addition, the forward motion and stop condition of the wheelchair make it difficult to discriminate between fault-free and hard fault conditions of the gyro, because in both these conditions, the gyro output is almost zero.
To cope with these problems, we switch the following model sets, according to the motion of the wheelchair: www.intechopen.com

Mechatronic Systems, Applications 150
In FDI for the wheel resolver, when the wheelchair is considered to stop (i.e., u left  0 and u right  0), model set MG 1 is selected; else, MG 2 is selected. In FDI for the gyro, when the wheelchair stops (i.e., u left  0 and u right  0) or moves straight (i.e., u left  u right ), model set MG 1 is selected; else, MG 2 is selected. The model-set-switching-based FDI algorithm is formulated based on a variable-structure-interacting-multimodel (VSIMM) estimator (Li, 2000;Hashimoto et al., 2003).

Fault Isolation of the Wheel Resolver and Wheel Motor
We consider a hard fault of the wheel motor as well as that of the wheel resolver. For a hard fault of the wheel motor, wheel rotation might stop completely. The hard fault of the wheel motor and that of the wheel resolver make the wheel-resolver output zero; thus, the IMMbased FDI mentioned in 3.1 cannot identify the faulty component (the wheel resolver or the wheel motor). In this subsection, when the IMM-based FDI detects the fault of the wheel unit, we identify the faulty component. A hard fault of the wheel motor and that of the wheel resolver cause a difference in the turning velocity of the wheelchair. When the hard fault of the wheel motor occurs, the turning velocity sensed by the gyro is almost the same as that calculated by the wheel resolver. On the other hand, when a hard fault in the wheel resolver occurs, the turning velocity sensed by the gyro is much different from that calculated by the wheel resolver. We therefore perform fault identification based on the following logic: then the wheel motor is faulty; else, the wheel resolver is faulty.
where b is the tread length of the wheelchair. h is the threshold; in our experiment, we set h as 0.01 [rad/s]. In principle, when a gyro fault occurs, it is impossible to discriminate between faults of the wheel resolver and the motor. For simultaneous faults of the wheel resolver and the motor, our FDI decides that the wheel resolver is faulty.

Scan Matching Based Velocity Estimate
In this section, we handle soft faults of the internal sensors that appear as changes in the sensor gain. A change in the sensor gain is caused by not only sensor faults but also various system component failures and environmental interactions. For example, a flat tire, wheel slippage, and soft wheel motor faults change the gain of the wheel resolver; therefore, their conditions are considered to be soft faults of the wheel resolver. In principle, it is necessary to determine the accurate linear and turning velocity of the wheelchair to detect soft faults of the internal sensors. We make use of laser scan matching with the fault-free LRS to estimate the velocity of the wheelchair. Our laser scan matching is based on typical point-to-point scan matching using an iterative closest point (ICP) algorithm (Besl & Mckay, 1992;Lu & Milios, 1997). In ICP-algorithm-based scan matching, the distance samples in the new laser scan are matched with those in the previous scan, so that the sum of squared distance can be minimized, and the velocity of the wheelchair is estimated. Before scan matching, we preprocess the scan image to remove erroneous distance samples (Diosi & Kleeman, 2007). This preprocessing consists of noise reduction, segmentation, and interpolation. The noise reduction is based on a median filter, and it replaces outliers of distance samples with suitable samples. The segmentation prevents incorrect interpolation between two disjoint distances. The interpolation allows estimation of distance samples at every angular resolution of 0.5 [deg] of the LRS. We determine the linear and turning velocities, , of the wheelchair by the weighted least-squares method; the cost function is Here, p i = (p ix , p iy ) T , where i = 1, 2,…, 361, is the distance sample in the current scan, while q j = (q jx , q jy ) T , where j = 1, 2,…, 361, is that in the previous scan. Each sample p i corresponds with the minimum distance sample q j of all samples in the previous scan. w i is the weight. R and T are the rotational matrix and the translational vector, respectively, given by  is the scanning period of the LRS; in our experimental The correspondence errors of distance samples of two successive scans affect the velocity estimate. To reduce the effect, we determine the weight w i according to the errors between the correspondence points: where d ij is the distance error between the new and previous scans. C is a constant; in our experiments, C = 0.1. From Eq. (9), the iterative least-squares method updates the wheelchair velocity In our experiments, the maximum iterative number of the velocity update is 20. The velocity estimate calculated by the iterative least-squares method is noisy, and it is smoothed using Kalman filter. One disadvantage of the ICP algorithm is that it converges slowly. To accelerate the convergence, we use dead-reckoning information as the initial velocity www.intechopen.com

FDI Algorithm
A soft fault appears as a change in the sensor gain, which deviates it from the fault-free condition; thus, we detect a soft fault by estimating the sensor gain. Sensor gain  is defined by condition free -fault the in output Sensor From this definition, when a sensor is fault free, the sensor gain equals unity. We estimate the sensor gain based on the wheelchair velocity estimated by laser scan matching. We assume that the state model of the sensor gain is given by where i = left (wheel), right (wheel), and gyro. From the inverse kinematics of the wheelchair velocity, the measurement model is derived: are the linear and turning velocities of the wheelchair, which are estimated by laser scan matching. The sensor gain is estimated based on Eqs. (13) and (14) via Kalman filter. A small change in the gain estimate always occurs due to wheel slippage, sensor noise, and so on. Thus, if the estimate of the sensor gain is far away from one (e.g., 0.7), the sensor is determined to be faulty. The stop condition of the wheelchair yields an incorrect estimate of the sensor gain, because it makes the right-handed side of Eq. (14) small. When the wheelchair moves straight, the turning velocity is very small, making it impossible to estimate the sensor gain. To better estimate the sensor gain, the following heuristic rules are incorporated into the fault decision making: Rule 1: If the control inputs of the two drive wheels are very small (i.e., u left  0 and u right  0), the gain estimates of all internal sensors in the previous cycle are held for the current cycle. Rule 2: If the control inputs of the two drive wheels are almost the same (i.e., u left  u right ), the gain estimate of the gyro in the previous cycle is held for the current cycle.
Because a hard sensor fault leads to = 0, we can detect the hard fault by estimating the sensor gain. However, the time delay in the hard fault detection by the sensor gain estimate is longer than that in the IMM-based hard fault detection. For this reason, we exploit the IMM estimator for hard fault detection.

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Model-Based Fault Detection and Isolation for a Powered Wheelchair 153

Fault Detection Algorithm
An LRS fault can be detected based on an error related to scan matching (Hashimoto et al., 2008a); if the current scan cannot match the previous scan, the LRS is determined to be faulty. For fault detection, we define the following cost function: are the rotational matrix and the translational vector, respectively, which contain the velocity estimate from laser scan matching. A fault is determined when J LRS > h LRS , where h LRS is a threshold. In detecting an LRS fault, Eq. (9) removes the correspondence points of large errors in two successive scan points. For this reason, we use Eq. (15) for detecting LRS faults. Noisy distance samples of the LRS may cause false detection, even though the LRS is fault free. To cope with this problem, the LRS is determined to be faulty, when J LRS > h LRS is always satisfied in several successive scans. In featureless environments (e.g., in long corridors), the corresponding pair between distance samples in two successive laser scans does not necessarily represent the same physical point in the environment, and the estimate of the wheel velocity becomes inaccurate, even though the LRS is fault free. To cope with this problem, we evaluate the distance samples by means of the Nieto approach (Nieto et al., 2007) and diagnose the LRS fault only in featured environments. In dynamic environments, moving objects and backgrounds occluded by the objects cause J LRS to be large, and false detections may occur. To cope with this problem, we detect the moving objects by the occupancy grid method (Hashimoto et al., 2006). As shown in Fig. 2, a grid map is represented in a reference coordinate frame  w (O w ;X w Y w ). The LRS measurements are mapped in  w and marked on the grid map. For each new cell of occupation in the current scan, the corresponding cell in the previous scan is checked. If that cell is marked, the cell in the current scan is considered a stationary object cell; else, it is a moving object cell. An object consisting of many moving object cells is determined as a moving object, and we remove the distance samples related to that moving object and backgrounds occluded by it when calculating the cost function J LRS . In our experiments, the cell size is set as 0.3 [m]  0.3 [m]. For mapping the laser image on the grid map, we use the wheelchair velocity estimated with laser scan matching.

Selection of Initial Velocity
In scan matching, we use dead-reckoning information as the initial velocity ) 0 ( x  to accelerate the convergence. A fault of an internal sensor thus causes J LRS to be large, even though the LRS is fault free. To cope with this problem, we define the following cost function: www.intechopen.com x  resulting from dead reckoning. If J DR < h DR , where h DR is a threshold, the internal sensor is assumed to be fault free, and we use dead-reckoning information as the initial velocity for scan matching. However, if J DR  h DR , the internal sensor is assumed to be faulty, and the velocity estimate in the previous scan is used as the initial velocity for scan matching in the new scan. When abrupt faults occur in the LRS, our algorithm detects the fault. However, incipient faults (a slow degradation of LRS performance), which may occur in the LRS in the real world, would allow scan matching, but estimate the wheelchair velocity inaccurately, causing incorrect fault detection. To cope with this problem, an alternative approach (Sundvall & Jensfelt, 2005) can be considered; the internal sensors estimate the wheelchair velocity by dead reckoning. The LRS also estimates it by scan matching. We thus can consider that the wheelchair is equipped with two different velocity providers (dead reckoning and laser scan matcher). Velocity estimates by fault-free providers yield similar values; whereas those of fault-free and faulty providers are inconsistent. This approach might be suitable for various fault patterns. However, this indicates only that something is going wrong in the two velocity providers; it cannot identify which provider is failing. If a wheelchair is equipped with three or more velocity providers, we can perform majorityvoting-logic-based FDI (Hashimoto et al., 2008b). The velocity estimates from the providers are compared, and the provider whose velocity estimate does not match the others is determined to be the faulty one.

Hard Fault of the Wheel Unit
The wheelchair was moved in a typical indoor environment. We conducted experiments in the following three scenarios: Scenario 1: All the internal sensors and LRS are fault free. It is clear from subfigure (d) that in scenarios 2 and 3, we can detect a hard fault of the left wheel unit exactly, based on the mode probability. In scenario 2, the turning velocity sensed by the gyro is much different from that calculated by the wheel resolvers. On the other hand, the turning velocity sensed by the gyro is almost the same as that calculated by the wheel resolvers in scenario 3. This difference enables identification of the component (resolver or motor) that fails.

Soft Fault of Internal and External Sensors
The wheelchair was moved in a typical indoor environment. Figure 6 shows the velocity profile of the wheelchair. Two people walked around in the environment. We set the thresholds related to scan matching at h LRS = h DR = 15 [m 2 ]. We conducted experiments in the following four scenarios: Scenario 4: All the internal sensors and LRS are fault free. Scenarios 5 and 6: The sensor gain of the right wheel resolver changes abruptly to 0.5 (scenario 5) and 0.8 (scenario 6), respectively, from 1.0 at 21 [s].
Scenarios 7: The sensor gain of the LRS changes abruptly to 0.8 from 1.0 at 30 [s]. Figures 7-10 show the experimental results. Because in scenarios 4, 5, and 6, the cost function J LRS is always less than the threshold h LRS , the LRS is determined to be fault free. Then, we estimate the sensor gain of the internal sensor, and then, based on the estimate, we detect a soft fault of the right wheel resolver, as shown in Figs. 8(c) and 9(c). In scenario 7 (Fig. 10), the cost function J DR is larger than the threshold h DR ; the internal sensor is assumed to be faulty, and the velocity estimate in the previous scan is used as the initial velocity for laser scan matching in the new scan. We also check the value of the cost function J LRS . Because J LRS > h LRS , the LRS is determined to be faulty.    For comparison, we conducted experiments using the FDI system without the movingobject detector, based on the occupancy grid method. Figure 11 shows the results (the values of the cost functions) in a fault-free condition of both the internal sensors and LRS. The FDI system without the moving-object detector causes false detection of the LRS fault because the values of the cost functions sometimes become larger than the thresholds. On the other hand, as shown in Fig. 7(a) and (b), our FDI system with the moving-object detector, provides the correct detection of the sensor state.

Conclusions
This chapter presented a model-based FDI for wheelchair sensors and actuators. Hard faults of the internal sensors and the wheel motors were detected based on the IMM estimator. Fault isolation of the wheel resolvers and the motors was achieved based on the information of the fault-free gyro. A soft fault of the internal sensors was diagnosed based on the velocity estimate of the wheelchair from laser scan matching, using the fault-free LRS. The LRS fault was detected based on errors related to scan matching. Abrupt faults of the LRS can be detected by our algorithm. However, incipient faults (a slow degradation of LRS performance), which can occur in the real world, allows scan matching, but estimates the wheelchair velocity inaccurately, and causes incorrect LRS fault detection. Our research effort is directed toward FDI for sensors and actuators in various fault patterns.