1. Why Roadheader Positioning Cannot Rely on an External Signal
A roadheader works in a semi-enclosed, development-type environment: roof support conditions are poor and the roadway cross-section is complex. Existing passive positioning technologies â such as UWB, RFID and Laser â all require deploying a number of positioning nodes and tags, and then infer the distance of a moving tag or target from a node indirectly from the propagation time of an optical or electrical signal, so as to achieve relative positioning of a moving object. In complex environments such as underground coal-mine roadways, passive positioning technology runs into numerous obstacles: difficult installation, large motion errors and short positioning range. For this reason, when it comes to the positioning problem of a roadway roadheader in a coal mine, active positioning based on inertial sensing has a natural advantage in resisting external interference.
Limited by the technical obstacles of repeatedly relocating and calibrating relay stations, such methods can all produce permanent indirect conversion errors when relay stations are moved multiple times, and therefore cannot meet the construction requirements of unmanned underground mining or the technical requirements of autonomous travel-positioning for a roadheader.
2. Why an Inertial Sensor Drifts: Where the Errors Come From
Deterministic and random errors
Because of assembly error, sensor sensitivity, ambient temperature and AD-conversion error, a real inertial sensor normally carries both deterministic and random errors. The deterministic errors of the sensor mainly include bias, scale-factor error, non-orthogonality error and temperature drift, while the random errors mainly include measurement Gaussian white noise and random walk.
In theory, when there is no external input, the output of the accelerometer and gyroscope should be zero. In practice, however, the real data output of the sensor has an offset error, called the bias error, or simply the bias. Because the conversion from a digital signal to a physical quantity carries a certain proportional error, the ratio between the true value of acceleration or angular rate and the sensor output value is called the scale-factor error. In addition, because of manufacturing-process and installation issues of multi-axis inertial sensors, the axes may not be strictly orthogonal to one another; this is called the non-orthogonality error, also known as the inter-axis error.
Errors that talk to each other
The errors of an inertial navigation system are strongly coupled with one another, forming a complex time-varying system. The roadheader carrier must therefore be decoupled under specific motion conditions so that independent poses and errors in the horizontal and vertical directions can be separated out.
The height channel has no bound
Pure inertial positioning carries a fundamental cumulative error in its height solution, so the height channel of a pure inertial navigation system is divergent. To address the height-divergence problem in roadheader inertial positioning, an odometer is introduced to aid the inertial solution. When it maintains good contact with the ground, the odometer can provide an excellent horizontal pose constraint for the inertial navigation system. The odometer can therefore be mounted on the output shaft of the roadheader’s crawler motor to improve inertial positioning performance.
Building the measurement
The Kalman filter state-estimation method consists of two main parts: the state-estimate update and the covariance update, in which the Kalman gain produced by the covariance update has an important influence on the state-estimate update. To determine the optimal state estimate of the system at a given moment, the initial state of the system and its covariance must first be determined. The system noise can generally be preset as the square of the angular-rate random-walk coefficient of the inertial gyroscope plus the square of the velocity random-walk coefficient of the accelerometer, while the measurement noise can generally be preset, together with the scale-error coefficient of the odometer, at three times the maximum deviation of the measurement information.
Tuning for two very different working states
Given the construction-process characteristics and working-environment characteristics of the roadheader carrier, Kalman-filter parameter tuning for the roadheader inertial positioning system can be divided into two cases. (a) In the cutting state, the machine body is treated as fixed to the ground; the strong interaction between the cutting head and the rock causes obvious body vibration, and the measurement-environment noise has a large influence. The measurement-noise matrix should then be enlarged and the system noise correspondingly reduced, matching the condition in which the roadheader’s state information is stable but the signal-to-noise ratio of the measurement information drops. (b) In the traveling state, the cutting head does not take part in cutting coal or rock and the body travels on an unpaved surface on its crawler running gear; on complex surfaces the accuracy of the system state model decreases while the measurement information can provide a good reference for state correction, so the system noise can be increased appropriately.
5. A Roadheader Stops and Starts: Zero-Velocity Soft-Feedback Correction
Most of the working cycle is downtime
When traveling along a roadway, a roadheader moves at roughly 5â10 m/min and every few meters it must stop to drag the cable; in addition, long stationary periods for roadway support work also occur frequently during the advance. It can be seen that the working motion of a roadheader contains a large amount of downtime, and during a stop the true velocity of the carrier is zero. At such a moment the velocity output by the roadheader inertial navigation system is the velocity error, and using this velocity error as the system measurement allows the state drift of the system to be constrained and compensated. On this basis a zero-velocity feedback method can be designed to correct the long-term velocity deviation of the roadheader inertial navigation system.
Hard zeroing is not enough
The traditional zero-velocity update correction rigidly sets the carrier velocity at a stationary instant directly to zero. Although this effectively suppresses velocity and displacement drift in the static phase, it ignores the velocity drift produced during the moving phase, so the correction of the roadheader carrier positioning error is incomplete. For the stop-start motion characteristics of the roadheader, therefore, a soft zero-velocity feedback correction method is proposed on the basis of the original hard zeroing method; it soft-zeros the continuous velocity, that is, while zeroing the velocity during the stationary period of the roadheader carrier, it simultaneously corrects the velocity drift in the moving interval using the mean value of the velocity drift of two adjacent stationary intervals. With the soft-zeroing form of zero-velocity feedback correction, the positioning accuracy of the roadheader carrier improved by 21.64%, further suppressing the long-term positioning drift of the inertial navigation system.
6. Hidden Errors Created by Vibration: Coning and Sculling
Coning error
Among the various coupling phenomena, when the pitch axis and the roll axis of the roadheader carrier each sense angular motion of the same frequency but different phase, the azimuth axis as a whole does not change its pointing, yet it still senses and outputs a constant angular-rate signal error â this is the coning-motion phenomenon. When the angular motions of the pitch axis and the roll axis differ in phase by 90 degrees, the induced angular-motion error of the roadheader’s azimuth axis is at its maximum.
To compensate the coning error of the roadheader carrier under vibration conditions, multiple sampling can usually be performed within the time interval, in which the angular increments of the sub-sampling periods are cross-multiplied with one another and summed with weights.
Sculling error
During its advance a roadheader not only exhibits angular vibration but also faces linear-vibration interference. When the roadheader’s pitch axis (x-axis) performs angular vibration at a fixed frequency while the roll axis (y-axis) simultaneously performs linear vibration of the same frequency and the same phase, a certain amount of velocity drift can be sensed on the azimuth axis (z-axis). This velocity error, produced by the coupling of angular vibration and linear vibration, is called the sculling error.
7. State Estimation Under Strong Nonlinearity: From EKF to UKF and CKF
The limits of a first-order approximation
In actual operation a roadway roadheader faces coupled interference from its own vibration, the cutting load and the roadway environment, so its motion takes on strongly nonlinear characteristics and its errors are coupled with one another. An ordinary Kalman filter is only suitable for the optimal estimation of linear systems, and even the extended Kalman filter is only suitable for weakly nonlinear systems that can be linearized by a first-order Taylor approximation.
Cubature as the closest practical approximation
Unlike the unscented Kalman filter, which uses deterministic sampling to generate 2n+1 sigma points to fit the probability density of the state distribution, the cubature Kalman filter, based on the third-order spherical-radial cubature rule, uses a set of cubature points to approximate the state mean and covariance of a nonlinear system with additive Gaussian noise, and is in theory the approximation algorithm currently closest to Bayesian filtering.
8. Measured Accuracy: What Inertial plus Odometer Actually Delivers
The roadheader pose solved by the pure inertial model diverges rapidly. The odometer can impose a certain constraint on the inertial information, and the roadheader trajectory solved by combining dead reckoning with the inertial solution shows no overall divergence, although its pose fluctuation and error remain large. The extended Kalman filter and the cubature Kalman filter, by contrast, obtain a comparatively accurate roadheader trajectory through optimal estimation.
In summary, within the roadheader’s daily advance range, when the pose of the roadheader is determined only by an odometer-aided inertial navigation system combined with a Kalman-filter method, positioning accuracy of roughly 0.25 m, 0.2 m and 0.3 m can be reached in the forward, lateral and vertical directions respectively, while the heading-angle error reaches degree-level accuracy. A relatively large heading deviation has a significant effect on both the cross-section forming quality of the roadway advance and the roadway direction, and easily leads to over-excavation or under-excavation of the cross-section.
9. The Vision Problem: Dust, Water Mist and Low Illumination
The roadway is a hostile camera environment
The roadway is a long, narrow space with a large turning radius. Its visual environment is dim with variable illumination, which produces large image noise, and the wall texture is complex â only the boundary between the heading face and the side walls, roof and floor is relatively distinct. The dust produced by coal and rock cutting is severe, blurring the roadheader’s visual images and drowning part of the features of equipment and structures. The dust-suppression water mist scatters and attenuates the illumination used for image acquisition, and airflow exchange such as face ventilation more easily causes diffuse-reflection illumination interference in the visual image, so that the images acquired by the roadheader visual positioning system suffer serious degradation.
Why ordinary dehazing fails here
The complex underground coal-mine dust-and-mist environment differs from ordinary outdoor and indoor environments: the space is long and narrow, illumination is low, and dust and mist are densely distributed, so the requirements are stricter and more difficult than ordinary dehazing. For a dim, dusty and misty coal-mine scene, there are usually multiple light sources, so the ambient illumination is usually not globally isotropic. In addition, the commonly used local maximum-pixel method tends to overestimate the global atmospheric light, and these two points cause colour distortion and halo artifacts around the light-source region in the output image.
10. The Fusion Architecture: Odometer-Aided Stereo Visual-Inertial Positioning
Why MSCKF instead of full SLAM
The underground coal-mine environment is complex. When traditional SLAM technology performs simultaneous localization and mapping for a roadheader, it continuously tracks and maintains a large number of feature points during the visual update; long-term operation of the system causes dimensionality explosion of the Kalman filter and consumes a great deal of computing resources. In the multi-state constraint Kalman filter (MSCKF) framework, by contrast, the position state of the feature points in each frame during the visual update is not treated as an estimated state of the filter â only the camera pose is estimated â which greatly reduces the dimension of the system state estimation and the consumption of computing resources.
Why error-state Kalman filtering
In the process of solving system states such as the position, velocity and attitude of the roadheader carrier from inertial measurement-unit data, various noises interfere, whereas using a Kalman filter to fuse visual information and correct the inertial positioning result can effectively suppress the integral drift. For this reason the error-state Kalman filter (ESKF) is introduced: the states that actually need to be estimated are divided into a nominal state and an error state. The nominal state is obtained by directly integrating the inertial unit data according to the motion model, and the Kalman filter is used to estimate the error state of the system; after estimation, the error state is used to correct the integral result of the nominal state, yielding the true state of the system.
Choosing Inertial Sensing for GNSS-Denied Machinery
Underground positioning is a problem of physics, not of signal coverage. In a roadway there is no satellite fix, and a passive node-and-tag network is fragile by construction. What remains is a layered inertial approach: calibrate the sensor and model its deterministic errors, constrain the drift with an odometer and zero-velocity feedback, compensate the vibration-induced coning and sculling errors, and fuse the result with stereo vision in an error-state filter so that the vision channel corrects the long-term drift while the inertial channel fills the frame gaps. Each layer removes one failure mode; together they keep a roadheader on course where no external signal reaches. When selecting an inertial sensor for this kind of machinery, the meaningful specifications are in-run bias stability, vibration rejection and a noise model that a Kalman filter can actually consume.