Mapped variable smoothing evolution method and device

The present inventions generally relate to methods and dedicated apparatuses outputting a variable mapped on a device orientation in a non-inertial reference system, with the device orientation being estimated using measurements of motion sensors (such as 3D accelerometers and gyroscopes) and a magnetometer or other similar sensors including cameras. A variable mapped on an orientation of a device is smoothed to have a gradual evolution by adjusting the estimated orientation of the device obtained via sensor fusion or other sensor processing to take into consideration a current measured angular velocity.

TECHNICAL FIELD

The present inventions generally relate to methods and dedicated apparatuses outputting a variable mapped on a device orientation in a non-inertial reference system, with the device orientation being estimated using measurements of motion sensors (such as 3D accelerometers and gyroscopes) and a magnetometer or other similar sensors including cameras.

BACKGROUND

As described in WO 2012/044964, yaw, roll and pitch angles of a device in a gravitational reference system may be evaluated using measurements of a magnetometer and other motion sensors (accelerometers, gyroscopes) attached to the device. These methods include:determining a measured 3D magnetic field, a roll, a pitch and a raw estimate of yaw in the body reference system based on the received measurements,extracting a local 3D magnetic field from the measured 3D magnetic field, andcalculating yaw angle of the body reference system in the gravitational reference system based on the extracted local 3D magnetic, the roll, the pitch and the raw estimate of yaw using at least two different methods,
wherein estimated errors of the roll, the pitch, and the extracted local 3D magnetic field affect an error of the yaw differently for the different methods.

A rotation matrix corresponding to the yaw, roll and pitch angles may be expressed as a quaternion (conversion between a rotation matrix corresponding to rotations around three orthogonal axes and a quaternion is known). The result of the sensor fusion methods described in WO 2012/044964 may be expressed as a quaternion.

Motion sensors may include gyroscopes or other sensors configured to measure angular velocities. The quaternion result from sensor fusion method (referred to as “fusion quaternion” hereinafter) is the best estimation of rotation angles (yaw, roll and pitch) based on all available sensor data. The sensor orientation (i.e., the output quaternion) may be mapped on a variable such as a position of a cursor on a screen or an image displayed to a user of a gaming system. Therefore, the output quaternion should be as accurate, stable (e.g., varying smoothly rather than “jumpy”) and consistent with all sensor indications as achievable. However, at certain moments, the angle estimations (which may be expressed as the fusion quaternion) do not agree with direct angular velocity measurements and, therefore, are not suitable for direct and indiscriminate use.

When a conflict between the fusion quaternion and the measured angular velocity arises, simple approaches to overcome this conflict are (1) to use the fusion quaternion directly or (2) to use measured angular velocity only.

One problem with the first approach (using the fusion quaternion directly) is that the fusion quaternion is not always continuous due to many reasons, such as magnetic field interference, linear acceleration, accelerometer saturation, etc. Another problem is that a fusion quaternion may keep moving while the device is still, due to delays introduced in the fusion process. Moreover, the fusion quaternion may also move in a direction different from that indicated by the angular velocity, due to delay or adjustment.

The second approach (using only angular velocity) is also problematic. The integration drift over a long period of time may cause a large misalignment between the integrated angular position and the device's true orientation.

Accordingly, it would be desirable to provide apparatuses and methods that advantageously make use of the fusion quaternion while also maintaining compatibility with measured angular velocity and avoid the problems identified above relative to the first and second approaches.

SUMMARY

Method and apparatuses according to various embodiments perform fusion quaternion smoothing in view of a measured angular velocity, and output a smoothed version of the fusion quaternion. The smoothed quaternion always moves in a manner that largely agrees with the measured angular velocity, while also matching the fusion quaternion in the long run. This quaternion smoothing has the advantage that the smoothed quaternion is consistent with the angular velocity within an angle limit and a scale limit, so that any discrepancy or inconsistency is not noticed by users viewing a cursor or an image determined using the smoothed quaternion. Also, the smoothed quaternion follows the fusion quaternion in the long run, eliminating long-term misalignment.

According to an embodiment, there is a method for smoothing evolution of a variable depending on an orientation of a device. The method includes determining an adjusted angular velocity based on a measured angular velocity and an estimated angular velocity so as to satisfy one or more predefined constraints. The method further includes determining a current value of the variable according to an adjusted estimate of the device's current orientation, obtained using the adjusted angular velocity.

According to another embodiment, there is a method for smoothing evolution of a variable depending on an orientation of a device. The method includes determining an expected orientation using a previous orientation of the device and a measured angular velocity. The method further includes determining a current value of the variable according to an adjusted estimate of the device's current orientation, obtained so as to be as close as possible to an estimate of the device's current orientation, but with an angle between the adjusted estimate of the current orientation and the expected orientation to be less than a maximum angle.

According to another embodiment, there is a gaming system configured to display an image to a user according to an orientation of a device. The gaming system includes (i) sensors mounted on the device and configured to acquire information leading to a measured angular velocity and an estimate of a current orientation of the device, and (ii) a data processing unit. The data processing unit is configured to determine (A) an adjusted angular velocity based on the measured angular velocity and the estimated angular velocity so as to satisfy one or more predefined constraints, (B) an adjusted estimate of the device's current orientation, obtained using the adjusted angular velocity, and (C) the image to be displayed to the user according to the adjusted estimate of the current orientation.

According to yet another embodiment, there is an information system controlled by orientation of a device. The system includes sensors mounted on the device and configured to acquire information leading to a measured angular velocity and an estimate of a current orientation of the device, and a data processing unit. The data processing unit is configured to determine (A) an adjusted angular velocity based on the measured angular velocity and the estimated angular velocity so as to satisfy one or more predefined constraints, (B) an adjusted estimate of the device's current orientation, obtained using the adjusted angular velocity, and (C) a position of a cursor on a screen based on the device's current orientation.

DETAILED DESCRIPTION

The following description of the exemplary embodiments refers to the accompanying drawings. The same reference numbers in different drawings identify the same or similar elements. The following detailed description does not limit the invention. The following embodiments are discussed, for simplicity, with regard to the terminology and structure of systems using sensor fusion in which a magnetometer and motion sensors are used to evaluate orientation of a device.

FIG. 1illustrates, as a starting point, the tip of a previous smoothed quaternion qs,n-1(here s stands for smoothed and n−1 indicates a previous moment). Sensor fusion method yields fusion quaternion qf,n(here f stands for fusion and n indicates the current moment, after n−1), but the measured angular velocity ωn(considering the time interval n−1 to n unitary here and hereinafter when referring to angular velocity) indicates instead an expected quaternion qω,n(here ω indicates that measured angular velocity was used to infer this quaternion and n for the current moment). Methods according to various embodiments described in this section determine a current smoothed quaternion qs,n(here s stands for smoothed and again n indicates the current moment) located between quaternions qf,nand qω,n. In various applications, a variable x (not shown) is mapped on the current smoothed quaternion qs,n. For example, variable x may be a cursor position on the screen. The evolution of variable x is smoothed (i.e., sudden changes are implemented gradually) by using smoothed quaternion qs,n.

FIG. 2is a flowchart illustrating a method200for smoothing evolution of a variable depending on an orientation of a device. Method200includes, at S210, determining an adjusted angular velocity (e.g., Ωs,ninFIG. 1) based on a measured angular velocity (ωn) and an estimated angular velocity (Ωf,n), so that the adjusted angular velocity satisfies one or more predefined constraints. Method200further includes, at S220, determining a current value (x) of the variable according to an adjusted (smoothed) estimate of the current orientation (qs,n) of the device obtained using adjusted angular velocity (Ωs,n). Details of these steps according to various embodiments are described below.

FIG. 3is a block diagram of a quaternion smoothing method300according to an embodiment. First, in block310, estimated angular velocity Ωf,nis determined based on the fusion quaternion qf,n(obtained based on magnetometer and motion sensor measurements using one of the methods described in WO 2012/044964) and the previous smoothed quaternion qs,n-1. This estimated angular velocity Ωf,nis, in general, different from the current angular velocity ωnmeasured, for example, by a gyroscope.

In block320, the adjusted angular velocity Ωs,nleading (when integrated) to the smoothed quaternion qs,nis determined as follows. The direction of adjusted angular velocity Ωs,nis set to match that of the estimated angular velocity Ωf,n, if the angle between estimated angular velocity Ωf,nand current (measured) angular velocity ωnis less than a predetermined angle limit θmax. The direction of adjusted angular velocity Ωs,nis set at θmaxfrom the current (measured) angular velocity ωn, if the angle between estimated angular velocity Ωf,nand current (measured) angular velocity ωnexceeds the predetermined angle limit θmax. The adjusted angular velocity Ωs,nis in the same plane as estimated angular velocity Ωf,nand current (measured) angular velocity ωn.

Further, the magnitude of estimated angular velocity Ωs,nis set equal to the magnitude of Ωf,n's component along the angular velocity's direction, if the ratio between the magnitude of Ωf,n's component and the angular velocity ωnis within a predetermined scale range, and the magnitude is set to a minimum/maximum value (depending upon which limit of the range is exceeded) otherwise.

Then, in block330, adjusted angular velocity Ωs,nis integrated from the previous smoothed quaternion qs,n-1to obtain the current smoothed quaternion qs,n. Due to the manner in which it is obtained, smoothed quaternion qs,nis always closer to the current fusion quaternion qf,nthan quaternion qω,n-1indicated by measured angular velocity ωn.

A few special situations require particular treatment. A first special situation is when the difference between angular velocity ωnand estimated angular velocity Ωf,nexceeds a predetermined threshold. In one embodiment, fusion quaternion qf,nis output in the first special situation. However, other embodiments proceed differently in this first special situation.

A second special situation is when the magnitude of angular velocity ωnis less than a minimum velocity ωmin(e.g., the user may intend to hold the device still). In one embodiment, the output quaternion qs,nis made equal to the previous smoothed quaternion qs,n-1, i.e., the smoothed quaternion angular velocity Ωs,nis zero. When angular velocity ωnexceeds the pre-determined minimum ωmin, the smoothed angular velocity Ωs,nincreases suddenly as illustrated by line410inFIG. 4. In one embodiment, this step increase may be smoothed to a more gradual increase as illustrated by curve420. However, other embodiments may proceed differently in this second situation.

Returning now toFIG. 3, tremor suppression (alias smoothed quaternion stabilization) block340is optional. The purpose of tremor suppression is to output a stationary quaternion q′s,nwhen the current smoothed quaternion qs,nis very close to the previous smoothed quaternion qs,n-1(i.e., the smoothed quaternion is approximately stationary). Such a situation (i.e., second special situation discussed above) occurs, for example, when a user intends to keep the device stationary, but small motions due to hand tremor are sensed. Stabilization is not necessary when the sensor readings are filtered to remove noise and user's tremor. However, in case of severe user's tremor or when sensor readings are not filtered, tremor suppression is beneficial especially when the output quaternion is used to determine a cursor position (i.e., the variable is the cursor's position).

An embodiment of block330for determining adjusted angular velocity Ωs,n(e.g., step S210inFIG. 2) is illustratedFIG. 5, and further explained inFIG. 6. Determining adjusted angular velocity Ωs,nstarts from measured angular velocity ωnand estimated angular velocity C (i.e., these are the block's inputs). This processing encompasses two aspects: determining the magnitude and the orientation of adjusted angular velocity. These determinations are subject to two constraints: (A) the difference between the magnitude of the adjusted angular velocity and the measured angular velocity to be limited (i.e., the magnitude is within a predetermined range relative to measured angular velocity's magnitude), and (B) an angle between the estimated angular velocity Ωf,nand the measured angular velocity ωnto be limited.

Block510calculates the scalar product of estimated angular velocity Ωf,nand measured angular velocity ωn. The scalar product may be used to determine the cosine of angle θ between estimated angular velocity and measured angular velocity:

Block520then calculates an initial scale a according to the formula (2):

The numerator of this ratio is the magnitude of the estimated angular velocity's projection along the measured angular velocity (i.e., from qs,n-1to point P inFIG. 1). Projecting estimated angular velocity Ωf,nis represented inFIG. 1using a dashed line, which starts at the tip of estimated angular velocity Ωf,n, is perpendicular to the measured angular velocity ωn, and ends in point P. The initial scale a may then be adjusted in block530to a scale value α′ within the range (MinScaling, MaxScaling):

The magnitude of adjusted angular velocity Ωs,nis then:
|Ωs,n=α′|ωn|.  (4)
FIG. 1illustrates the situation in which α=α′ and, therefore, the locus of the adjusted angular velocity's tip is the dashed portion of a circle with the center in qs,n-1and passing through point P.

To determine the direction of the adjusted angular velocity, in block540, a set of unit vectors is defined as illustrated inFIG. 6. Unit vector v0is along the measured angular velocity ωn. Unit vector v1is along the estimated angular velocity Ωf,n. In other words, measured angular velocity ωnand estimated angular velocity Ωf,nmay be written as:
ωn=v0|ωn|  (5)
Ωf,n=v1|Ωf,n|.  (6)

Unit vector v2is the normalized component of vector v1on a direction perpendicular to vector v0. Before normalization, vector v1's component on the direction perpendicular to vector v0is v2u, and it is equal to the difference between the vector v1and vector v0's projection along v1(i.e., v1cos θ):

Thus, unit vector v is coplanar to unit vectors v0, v1, at θmaxfrom unit vector v0toward unit vectors v1. Other alternative methods may be used to obtain unit vector v.

In one embodiment, at block550, if angle θ between estimated angular velocity Ωf,nand measured angular velocity ωnis less than θmaxthen v=v1. Otherwise (if angle θ exceeds θmax) v is calculated with formula (9).

At block560, outputs of blocks530and550(i.e., magnitude and orientation) are combined to obtain adjusted angular velocity Ωs,nas:
Ωs,n=|Ωs,n|·v.(10)

The above-discussed methods for determining adjusted angular velocity can also be used when smoothed angular position is not represented by quaternions, but by Euler angles or rotation matrices.

The amount of quaternion difference between smoothed quaternion qs,nand fusion quaternion qf,nis influenced by parameters θmax, MinScaling and MaxScaling. In some embodiments, these parameters may be fixed, but in other embodiments these parameters may be dynamically adjusted to obtain a smoother result. For example, the adjustment may be made larger when the difference between estimated angular velocity and measured angular velocity is large.

Under some circumstances (e.g., dramatic changes of the fusion quaternion q), the adjustment might be in one direction for a first moment, and change to the opposite direction for a second (next) moment. To reduce radical and frequent changes, in one embodiment, the variation of the quaternion adjustment from one moment to the next may be limited.

Returning now toFIG. 3, in one embodiment, optional tremor suppression block340operates based on a circular backlash algorithm. Although the quaternion is a 4D variable, the concept of circular backlash is illustrated inFIG. 7as a 2D drawing. Circle710has as its center the previous stabilized quaternion q′s,n-1and a radius m (i.e., a maximum angular velocity multiplied by an unitary time interval from n−1 to n). If the current adjusted quaternion qs,nis inside circle710, then the stabilized quaternion q′s,nis made equal to the previous stabilized quaternion q′s,n-1(i.e., q′s,n=q′s,n-1) so that the stabilized quaternion q′s,nand the circle surrounding it remain the same. If the current adjusted quaternion qs,nis outside circle710, a new circle720is shifted relative to circle710with the least amount necessary to cover qs,n. Stabilized quaternion q′s,nis the center of this new circle720.

Thus, if qs,n−q′s,n-1<m (i.e., qs,nis inside the circle), q′s,n−q′s,n-1=0, otherwise q′s,n−q′s,n-1=qs,n−q′s,n-1−m (i.e., the output quaternion q′s,nand the circle are shifted with the least amount necessary to cover qs,n).

The current smoothed quaternion qs,nmay be obtained in the quaternion domain directly, without using angular velocities (i.e., skipping blocks310and330inFIG. 3).FIG. 8is a flowchart of a method800according to an embodiment, in which an expected orientation qω,nis determined using measured angular velocity ωnand a previous orientation qs,n-1, at S810. Then, at S820, method800includes determining a current value x of the variable according to an adjusted estimate of the current orientation qs,nof the device which is obtained so as to minimize the angle between it and the estimate of a current orientation qf,nof the device (e.g., according to the sensor fusion), while satisfying the requirement that the angle φ between the adjusted estimate of current orientation qs,nand expected orientation qω,nbe less than a maximum angle ωmax. For example, if the angular difference φ between qf,nand qω,nis less than φmax, then qs,n=qf,n, and otherwise, qs,nmay be interpolated as a weighted average between qf,n(e.g., weighted by φmax/φ) and qω,n(e.g., weighted by 1−φmax/φ). The accurate interpolation for quaternion is a spherical linear interpolation, but the following linear approximation may be used instead:

qs,n=qf,n⁢wf+qω,n⁡(1-wf)⁢⁢where⁢⁢wf=min⁡(1,φmaxφ).(11)
The angle difference limit φmaxmay be a monotonic function of the measured angular velocity's magnitude |ωn|.

A dedicated apparatus/system may be used to implement the above-described methods. This dedicated apparatus/system may be part of a gaming system or an information system controlled by orientation of a device. For example,FIG. 9illustrates a block diagram of such a system900. System900includes sensors910(e.g., an accelerometer, a gyroscope and a magnetometer) mounted on the device and configured to acquire information leading to a measured angular velocity ωnand an estimate of a current orientation qf,nof the device. System900further includes data processing unit920configured to determine (A) an adjusted angular velocity Ωs,nbased on measured angular velocity ωnand estimated angular velocity Ωf,nto satisfy one or more predefined constraints, and (B) an adjusted estimate of current orientation qs,nof the device obtained using adjusted angular velocity Ωs,n. The adjusted estimate of current orientation is mapped on variable x that may be used by a hardware component distinct from the device. Data processing unit920may be located on the device or remote, for example, on the hardware component (e.g., a display) using the variable x.

If system900is a gaming system configured to display an image to a user according to an orientation of a device (e.g., a handheld device), then data processing unit920is further configured to determine the image to be displayed according to the adjusted estimate of current orientation qs,n.

If system900is an information system controlled by orientation of a device, then data processing unit920is further configured to determine the position of a cursor on a screen based on the current orientation qs,nof the device.

System900may also include a memory930storing a computer program product which, when executed by a data processing unit, executes any of the above-described methods. The memory may be any suitable computer-readable medium, including hard disks, CD-ROMs, digital versatile disc (DVD), optical storage devices, or magnetic storage devices such as a floppy disk or magnetic tape. Other non-limiting examples of computer-readable media include flash-type memories or other known memories. Accordingly, the exemplary embodiments may take the form of an entirely hardware embodiment or an embodiment combining hardware and software aspects.

The disclosed exemplary embodiments provide methods and apparatuses for determining an adjusted and (optionally) stabilized orientation of a device in a non-inertial reference system using measurements of motion sensors (such as 3D accelerometers and gyroscopes) and a magnetometer. It should be understood that this description is not intended to limit the invention. On the contrary, the exemplary embodiments are intended to cover alternatives, modifications and equivalents, which are included in the spirit and scope of the invention. Other sensors could be used to measure orientations including angular position sensors, tilt sensors, cameras and so on. The various embodiments can be used when those alternate sensors are used. Further, in the detailed description of the exemplary embodiments, numerous specific details are set forth in order to provide a comprehensive understanding of the inventions. However, one skilled in the art would understand that various embodiments may be practiced without such specific details. Orientation and angular velocity are exemplary features here, but similar methods to smooth a variable in a way that minimizes distress to either humans or other equipment or algorithms downstream. For example, similar methods could apply to translational movement's position and velocity. The variable does not have to be angular position or velocity nor does the targeted consumer have to be a human being.