Quaternion Rotation

Rotate vector by quaternion

• Library:

• Aerospace Blockset / Utilities / Math Operations

• 

Description

The Quaternion Rotation block rotates a vector by a quaternion. Aerospace Blockset™ uses quaternions that are defined using the scalar-first convention. This block normalizes all quaternion inputs. For the equations used for the quaternion, vector, and rotated vector, see Algorithms.

Ports

Input

q — Quaternion

quaternion | vector

Quaternions in the form of [q₀, r₀, ..., q₁, r₁, ... , q₂, r₂, ... , q₃, r₃, ...], specified as a quaternion or vector of quaternions.

Data Types: double

vec — Vector

vector | vector of vectors

Vector or vector of vectors in the form of [v₁, u₁, ... , v₂, u₂, ... , v₃, u₃, ...].

Data Types: double

Output

vec_rot — Rotated quaternion

rotated quaternion | vector of rotated quaternions

Rotated vector or vector of rotated vectors.

Data Types: double

Model Examples

Developing the Apollo Lunar Module Digital Autopilot

"Working on the design of the Lunar Module digital autopilot was the highlight of my career as an engineer. When Neil Armstrong stepped off the LM (Lunar Module) onto the moon's surface, every engineer who contributed to the Apollo program felt a sense of pride and accomplishment. We had succeeded in our goal. We had developed technology that never existed before, and through hard work and meticulous attention to detail, we had created a system that worked flawlessly." -Richard J. Gran, The Apollo 11 Moon Landing: Spacecraft Design Then and Now

Open Live Script

Algorithms

The quaternion has the form of

$$q=q_0+i{q}_1+j{q}_2+k{q}_3.$$

The vector has the form of

$$v=i{v}_1+j{v}_2+k{v}_3.$$

The rotated vector has the form of

$$v^{\prime }=\left[\begin{array}{c}{v}_1{}^{\prime }\\ v_2{}^{\prime }\\ v_3{}^{\prime }\end{array}\right]=\left[\begin{array}{ccc}(1-2q_2^2-2q_3^2)& 2(q_1{q}_2+q_0{q}_3)& 2(q_1{q}_3-q_0{q}_2)\\ 2(q_1{q}_2-q_0{q}_3)& (1-2q_1^2-2q_3^2)& 2(q_2{q}_3+q_0{q}_1)\\ 2(q_1{q}_3+q_0{q}_2)& 2(q_2{q}_3-q_0{q}_1)& (1-2q_1^2-2q_2^2)\end{array}\right]\left[\begin{array}{c}{v}_1\\ v_2\\ v_3\end{array}\right]$$

References

[1] Stevens, Brian L., Frank L. Lewis. Aircraft Control and Simulation, Second Edition. Hoboken, NJ: Wiley–Interscience.

[2] Diebel, James. "Representing Attitude: Euler Angles, Unit Quaternions, and Rotation Vectors." Stanford University, Stanford, California, 2006.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a