Determining angular acceleration
Disclosed herein are systems and methods for calculating angular acceleration based on inertial data using two or more inertial measurement units (IMUs). The calculated angular acceleration may be used to estimate a position of a wearable head device comprising the IMUs. Virtual content may be presented based on the position of the wearable head device. In some embodiments, a first IMU and a second IMU share a coincident measurement axis.
1. A system comprising:
a first inertial measurement unit and a second inertial measurement unit, wherein the second inertial measurement unit is disposed at a fixed position with respect to the first inertial measurement unit; and
one or more processors configured to perform a method comprising:
receiving first inertial data via the first inertial measurement unit;
receiving second inertial data via the second inertial measurement unit;
calculating an angular acceleration based on the first inertial data and based further on the second inertial data;
estimating a position of a wearable head device based on the angular acceleration, wherein:
the estimating the position of the wearable head device based on the angular acceleration comprises calculating a pre-integration term based on the angular acceleration, and
the pre-integration term relates a first state of the wearable head device to a second state of the wearable head device; and
performing an operation based on the position of the wearable head device.
2. The system of claim 1 , wherein the calculating the pre-integration term comprises determining a single relative motion constraint based on the first inertial data.
3. The system of claim 1 , wherein the method further comprises estimating the position further based on the pre-integration term.
4. The system of claim 1 , wherein the method further comprises performing simultaneous localization and mapping via the pre-integration term.
5. The system of claim 1 , wherein the method further comprises determining a relative motion constraint between the first state and the second state based on the pre-integration term.
6. The system of claim 1 , wherein each of the first state and the second state comprises a respective keyrig pose.
7. The system of claim 1 , wherein each of the first state and the second state comprises a respective quaternion.
8. The system of claim 1 , wherein the estimating the position of the wearable head device is further based on bias data associated with the first inertial measurement unit.
9. The system of claim 1 , wherein the method further comprises predicting a second position of the wearable head device based on the angular acceleration and based further on the position of the wearable head device.
10. The system of claim 1 , wherein the operation comprises presenting virtual content via the wearable head device.
11. The system of claim 10 , wherein a position of the virtual content is determined based on the position of the wearable head device.
12. The system of claim 1 , wherein each of the first state and the second state comprises respective position data and respective velocity data.
13. A method comprising:
receiving first inertial data via a first inertial measurement unit;
receiving second inertial data via a second inertial measurement unit, wherein the second inertial measurement unit is disposed at a fixed position with respect to the first inertial measurement unit;
calculating an angular acceleration based on the first inertial data and based further on the second inertial data;
estimating a position of a wearable head device based on the angular acceleration,
wherein:
the estimating the position of the wearable head device based on the angular acceleration comprises calculating a pre-integration term based on the angular acceleration, and
the pre-integration term relates a first state of the wearable head device to a second state of the wearable head device; and
performing an operation based on the position of the wearable head device.
14. The method of claim 13 , wherein the calculating the pre-integration term comprises determining a single relative motion constraint based on the first inertial data.
15. The method of claim 13 , further comprising estimating the position further based on the pre-integration term.
16. The method of claim 13 , further comprising performing simultaneous localization and mapping via the pre-integration term.
17. The method of claim 13 , further comprising determining a relative motion constraint between the first state and the second state based on the pre-integration term.
18. The method of claim 13 , further comprising predicting a second position of the wearable head device based on the angular acceleration and based further on the position of the wearable head device.
19. The method of claim 13 , wherein the operation comprises presenting virtual content via the wearable head device.
20. A non-transitory computer-readable medium storing one or more instructions, which, when executed by one or more processors of an electronic device, cause the one or more processors to perform a method comprising:
receiving first inertial data via a first inertial measurement unit;
receiving second inertial data via a second inertial measurement unit, wherein the second inertial measurement unit is disposed at a fixed position with respect to the first inertial measurement unit;
calculating an angular acceleration based on the first inertial data and based further on the second inertial data;
estimating a position of a wearable head device based on the angular acceleration, wherein:
the estimating the position of the wearable head device based on the angular acceleration comprises calculating a pre-integration term based on the angular acceleration, and
the pre-integration term relates a first state of the wearable head device to a second state of the wearable head device; and
performing an operation based on the position of the wearable head device.