# US 10,371,522 B2 · Iterative estimation of centripetal accelerations of inertial measurement units in kinematic chains

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- Number: US 10,371,522 B2
- Document ID: US10371522B2
- Status: Granted
- Kind: B2
- Application number: 15/424,356
- Filed: 2017-02-03
- Published: 2018-08-09
- Granted: 2019-08-06
- Earliest claimed: 2017-02-03
- Assignees: Caterpillar Trimble Control Technologies LLC
- Applicants: Caterpillar Trimble Control Technologies LLC
- Inventors: Nima Alam
- Web page: https://patentgrep.com/patent/US10371522B2

## CPC

- G01C 19/5776: Signal processing not specific to any of the devices covered by groups G01C19/5607 - G01C19/5719
- G01P 3/44: for measuring angular speed (G01P3/56 takes precedence)
- G01P 15/08: with conversion into electric or magnetic values
- G01P 15/18: in two or more dimensions
- G01C: MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY (measuring liquid level G01F; radio navigation, determining distance or velocity by use of propagation effects, e.g. Doppler effects, propagation time, of radio waves, analogous arrangements using other waves G01S)
- G01P: MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT (measuring or recording blood flow A61B5/02, A61B8/06; monitoring speed or deceleration of electrically-propelled vehicles B60L3/00; vehicle lighting systems adapted to indicate speed B60Q1/54; determining position or course in navigation, measuring ground distance in geodesy or surveying G01C; combined measuring devices for measuring two or more variables of movement G01C23/00; measuring velocity of sound G01H; measuring velocity of light G01J7/00; measuring direction or velocity of solid objects by reception or emission of radiowaves or other waves and based on propagation effects, e.g. Doppler effect, propagation time, direction of propagation, G01S; measuring speed of nuclear radiation G01T; measuring acceleration of gravity G01V; {measuring or recording the speed of trains B61L23/00; speed indicators incorporated in motor vehicles B60K35/00; measuring frequency or phase G01R; traffic control G08G})

## Abstract

A method for determining centripetal accelerations of pivotally coupled rigid bodies arranged in a series, where the series includes a rigid body arranged between a previous rigid body and a next rigid body, includes determining the centripetal acceleration of the next rigid body and the centripetal acceleration at an inertial measurement unit (IMU) coupled to the next rigid body based on measurements and calculated parameters from the rigid body and the next rigid body. The centripetal acceleration of the next rigid body and the centripetal acceleration at the IMU coupled to the next rigid body are determined without using measurements or calculated parameters from the previous rigid body.

## Claims

### Claim 1

A method of compensating for centripetal accelerations of inertial measurement units (IMUs) disposed on separate but coupled rigid bodies, the method comprising:
determining a centripetal acceleration of a rigid body at a pivot point between the rigid body and a previous rigid body, the rigid body having an IMU coupled thereto, and the previous rigid body having another IMU coupled thereto, wherein the centripetal acceleration of the rigid body is determined based on:
an angular velocity of the previous rigid body;
an angular acceleration of the previous rigid body;
a centripetal acceleration of the previous rigid body;
a global angular velocity skew matrix of the previous rigid body;
a position of a pivot point between the rigid body and a next rigid body relative to the pivot point between the rigid body and the previous rigid body; and
a matrix for rotation between the previous rigid body and the rigid body;
determining a centripetal acceleration at the IMU of the rigid body, wherein the centripetal acceleration at the IMU of the rigid body is determined based on:
the centripetal acceleration of the rigid body;
a location of the IMU on the rigid body;
an angular acceleration of the rigid body; and
a global angular velocity skew matrix of the rigid body;
determining a relative angle between the rigid body and the previous rigid body based on a measured acceleration at the IMU of the rigid body, the centripetal acceleration at the IMU of the rigid body, a measured acceleration at the IMU of the previous rigid body, and a centripetal acceleration at the IMU of the previous rigid body;
determining a centripetal acceleration of a next rigid body at a pivot point between the next rigid body and the rigid body, the rigid body arranged between the previous rigid body and the next rigid body, the next rigid body having another IMU coupled thereto, wherein the centripetal acceleration of the next rigid body is determined based on:
an angular velocity of the rigid body;
the angular acceleration of the rigid body;
the centripetal acceleration of the rigid body;
the global angular velocity skew matrix of the rigid body;
a position of the pivot point between the next rigid body and a following rigid body relative to the pivot point between the next rigid body and the rigid body, wherein the following rigid body is after the next rigid body in a series; and
a matrix for rotation between the rigid body and the next rigid body;
determining a centripetal acceleration at the IMU of the next rigid body, wherein the centripetal acceleration at the IMU of the next rigid body is determined based on:
the centripetal acceleration of the next rigid body;
a location of the IMU on the next rigid body;
an angular acceleration of the next rigid body; and
a global angular velocity skew matrix of the next rigid body;
determining a relative angle between the next rigid body and the rigid body based on a measured acceleration at the IMU of the next rigid body, the centripetal acceleration at the IMU of the next rigid body, the measured acceleration at the IMU of the rigid body, and the centripetal acceleration at the IMU of the rigid body.

### Claim 2 (depends on 1)

The method of claim 1 wherein the centripetal acceleration of the next rigid body and the centripetal acceleration at the IMU of the next rigid body are determined without using the angular velocity of the previous rigid body as an input.

### Claim 3 (depends on 1)

The method of claim 1 wherein the centripetal acceleration of the next rigid body and the centripetal acceleration at the IMU of the next rigid body are determined without using measurements from the previous rigid body as inputs.

### Claim 4 (depends on 1)

The method of claim 1 wherein the centripetal acceleration of the next rigid body and the centripetal acceleration at the IMU of the next rigid body are determined without using calculated parameters from the previous rigid body as inputs.

### Claim 5 (depends on 1)

The method of claim 1 wherein the position of the pivot point between the rigid body and the next rigid body relative to the pivot point between the rigid body and the previous rigid body is a vector extending from the pivot point between the rigid body and the previous rigid body to the pivot point between the rigid body and the next rigid body.

### Claim 6 (depends on 1)

The method of claim 1 wherein the location of the IMU on the rigid body is a vector extending from the pivot point between the rigid body and the previous rigid body to the location of the IMU on the rigid body.

### Claim 7 (depends on 1)

The method of claim 1 wherein the global angular velocity skew matrix of the rigid body is determined based on the matrix for rotation between the previous rigid body and the rigid body, the global angular velocity skew matrix of the previous rigid body, and a local angular velocity skew matrix of the rigid body.

### Claim 8 (depends on 7)

The method of claim 7 wherein the local angular velocity skew matrix of the rigid body is determined based on a rotation rate of the rigid body around the pivot point between the rigid body and the previous rigid body.

### Claim 9 (depends on 8)

The method of claim 8 wherein the rotation rate of the rigid body around the pivot point between the rigid body and the previous rigid body is determined based on the angular velocity of rigid body, the matrix for rotation between the previous rigid body and the rigid body, and the angular velocity of the previous rigid body.

### Claim 10

A method for determining angles between a series of separate but coupled rigid bodies, the method comprising:
determining a centripetal acceleration of a rigid body, the centripetal acceleration of the rigid body based in part on an angular velocity of a previous rigid body, the previous rigid body being pivotally coupled to the rigid body;
determining a centripetal acceleration at an inertial measurement unit (IMU) coupled to the rigid body, the centripetal acceleration at the IMU based in part on the centripetal acceleration of the rigid body;
determining a relative angle between the rigid body and the previous rigid body based on a measured acceleration at the IMU, the centripetal acceleration at the IMU, a measured acceleration at an IMU coupled to the previous rigid body, and a centripetal acceleration at the IMU coupled to the previous rigid body;
determining a centripetal acceleration of a next rigid body, the centripetal acceleration of the next rigid body based in part on an angular velocity of the rigid body, the rigid body being pivotally coupled to the next rigid body;
determining a centripetal acceleration at a next IMU coupled to the next rigid body, the centripetal acceleration at the next IMU based in part on the centripetal acceleration of the next rigid body, wherein the centripetal acceleration of the next rigid body and the centripetal acceleration at the next IMU are determined without using the angular velocity of the previous rigid body as an input; and
determining a relative angle between the next rigid body and the rigid body based on a measured acceleration at the next IMU, the centripetal acceleration at the next IMU, a measured acceleration at the IMU coupled to the rigid body, and the centripetal acceleration at the IMU coupled to the rigid body.

### Claim 11 (depends on 10)

The method of claim 10 wherein the centripetal acceleration of the next rigid body and the centripetal acceleration at the next IMU are determined without using measurements from the previous rigid body as inputs.

### Claim 12 (depends on 10)

The method of claim 10 wherein the centripetal acceleration of the next rigid body and the centripetal acceleration at the next IMU are determined without using calculated parameters from the previous rigid body as inputs.

### Claim 13 (depends on 10)

The method of claim 10 wherein the centripetal acceleration of the next rigid body is also based on an angular acceleration of the rigid body, the centripetal acceleration of the rigid body, a global angular velocity skew matrix of the rigid body, a position of the pivot point between the next rigid body and a following rigid body relative to the pivot point between the next rigid body and the rigid body, and a matrix for rotation between the rigid body and the next rigid body.

### Claim 14 (depends on 10)

The method of claim 10 wherein the centripetal acceleration at the next IMU coupled to the next rigid body is also based on the centripetal acceleration of the next rigid body, a location of the next IMU on the next rigid body, an angular acceleration of the next rigid body, and a global angular velocity skew matrix of the next rigid body.

### Claim 15

A method for determining centripetal accelerations of pivotally coupled rigid bodies arranged in a series, the series including a rigid body arranged between a previous rigid body and a next rigid body, the method comprising:
determining the centripetal acceleration of the next rigid body and the centripetal acceleration at an inertial measurement unit (IMU) coupled to the next rigid body based on measurements and calculated parameters from the rigid body and the next rigid body, wherein the centripetal acceleration of the next rigid body and the centripetal acceleration at the IMU coupled to the next rigid body are determined without using measurements or calculated parameters from the previous rigid body.

### Claim 16 (depends on 15)

The method of claim 15 wherein the centripetal acceleration of the next rigid body is determined based on an angular velocity of the rigid body, an angular acceleration of the rigid body, a centripetal acceleration of the rigid body, a global angular velocity skew matrix of the rigid body, a position of the pivot point between the next rigid body and a following rigid body relative to the pivot point between the next rigid body and the rigid body, and a matrix for rotation between the rigid body and the next rigid body.

### Claim 17 (depends on 15)

The method of claim 15 wherein the centripetal acceleration at the IMU coupled to the next rigid body is determined based on the centripetal acceleration of the next rigid body, a location of the IMU on the next rigid body, an angular acceleration of the next rigid body, and a global angular velocity skew matrix of the next rigid body.

### Claim 18 (depends on 15)

The method of claim 15 further comprising determining a relative angle between the next rigid body and the rigid body based at least in part of the centripetal acceleration at the next IMU.

### Claim 19 (depends on 15)

The method of claim 15 further comprising determining the centripetal acceleration of the rigid body and the centripetal acceleration at an IMU coupled to the rigid body based on measurements and calculated parameters from the previous rigid body and the rigid body, wherein the centripetal acceleration of the rigid body and the centripetal acceleration at the IMU coupled to the rigid body are determined without using measurements or calculated parameters from rigid bodies before the previous rigid body in the series.

### Claim 20 (depends on 15)

A method for determining angles between pivotally coupled rigid bodies arranged in a series, the series including a rigid body arranged between a previous rigid body and a next rigid body, the method comprising:
determining a centripetal acceleration of the rigid body and a centripetal acceleration at an inertial measurement unit (IMU) coupled to the rigid body;
determining a relative angle between the rigid body and the previous rigid body based on a measured acceleration at the IMU, the centripetal acceleration at the IMU, a measured acceleration at an IMU coupled to the previous rigid body, and a centripetal acceleration at the IMU coupled to the previous rigid body;
determining the centripetal acceleration of the next rigid body and the centripetal acceleration at an IMU coupled to the next rigid body according to the method recited by claim 15, and
determining a relative angle between the next rigid body and the rigid body based on a measured acceleration at the IMU coupled to the next rigid body, the centripetal acceleration at the IMU coupled to the next rigid body, a measured acceleration at the IMU coupled to the rigid body, and a centripetal acceleration at the IMU coupled to the rigid body.