ROS IMU数据处理：madgwick滤波算法详解

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"ROS imu_filter_madgwick 功能包主要涉及的是针对IMU（惯性测量单元）数据的处理，使用了一种基于梯度下降算法的创新性姿态估计方法，特别适合于康复应用中的可穿戴人体运动追踪系统。该算法适用于包含三轴陀螺仪、加速度计和磁力计的IMU，以及具有磁力补偿功能的MARG（磁力角速率和重力）传感器阵列。" ROS imu_filter_madgwick 是一个在ROS（Robot Operating System）中广泛使用的功能包，其核心任务是对来自IMU的数据进行滤波和校正，以提高姿态估计的准确性和稳定性。这个功能包采用了一种由Sebastian O. H. Madgwick等人提出的高效算法，它利用四元数表示法来融合陀螺仪、加速度计和（可选的）磁力计的数据。四元数是一种数学工具，常用于描述3D空间中的旋转。在imu_filter_madgwick中，四元数被用来表示IMU传感器的相对姿态，这样可以有效地融合来自不同传感器的信号，尤其是当这些传感器存在噪声或者受到外界干扰时。该算法的关键在于使用梯度下降法，这是一种优化算法，通过迭代逼近最小化误差的方法来更新姿态估计。具体来说，该算法首先计算出陀螺仪测量误差的方向，然后通过四元数导数的形式，将加速度计和磁力计的数据纳入考虑，以校正这个误差。由于磁力计数据可能会受到地球磁场变化和周围环境磁场干扰的影响，MARG传感器阵列的引入能够补偿这种磁力扭曲，从而提供更准确的方位信息。在实际应用中，imu_filter_madgwick的表现已经通过与商用姿态传感器和光学测量系统的参考数据进行对比评估。实验结果证明了该算法的性能优势，并且与基于Kalman滤波的传统算法进行了基准测试，显示了其在某些场景下的优越性。 ROS imu_filter_madgwick 功能包提供了高效的IMU数据处理能力，尤其适用于需要实时、精确姿态估计的机器人和穿戴设备应用。通过结合多种传感器数据并使用创新的优化算法，它能够在复杂环境中提供稳定可靠的姿态信息，对于导航、运动控制和姿态跟踪等领域具有重要意义。

Estimation of IMU and MARG orientation using a

gradient descent algorithm

Sebastian O.H. Madgwick, Andrew J.L. Harrison, Ravi Vaidyanathan

Abstract—This paper presents a novel orientation algorithm

designed to support a computationally efﬁcient, wearable inertial

human motion tracking system for rehabilitation applications. It

is applicable to inertial measurement units (IMUs) consisting of

tri-axis gyroscopes and accelerometers, and magnetic angular

rate and gravity (MARG) sensor arrays that also include tri-axis

magnetometers. The MARG implementation incorporates mag-

netic distortion compensation. The algorithm uses a quaternion

representation, allowing accelerometer and magnetometer data to

be used in an analytically derived and optimised gradient descent

algorithm to compute the direction of the gyroscope measurement

error as a quaternion derivative. Performance has been evaluated

empirically using a commercially available orientation sensor

and reference measurements of orientation obtained using an

optical measurement system. Performance was also benchmarked

against the propriety Kalman-based algorithm of orientation

sensor. Results indicate the algorithm achieves levels of accuracy

matching that of the Kalman based algorithm; < 0.8

◦

static

RMS error, < 1.7

◦

dynamic RMS error. The implications of the

low computational load and ability to operate at small sampling

rates signiﬁcantly reduces the hardware and power necessary

for wearable inertial movement tracking, enabling the creation

of lightweight, inexpensive systems capable of functioning for

extended periods of time.

I. INTRODUCTION

The accurate measurement of orientation plays a critical

role in a range of ﬁelds including: aerospace [1], robotics [2],

[3], navigation [4], [5] and human motion analysis [6], [7]

and machine interaction [8]. In rehabilitation, motion tracking

is vital enabling technology, in particular for monitoring

outside clinical environs; ideally, a patient’s activities could

be continuously monitored, and subsequently corrected. While

extensive work has been performed for motion tracking for

rehabilitation, an unobtrusive, wearable system capable of

logging data for extended periods of time has yet to be

realized. Existing systems often require a laptop or handheld

PC to be carried by the subject due to the processing, data

storage, and power requirements of the sensory equipment.

This is not practical outside of a laboratory environment, thus

detailed data may only be obtained for short periods of time

for a limited range of subject’s motion. More precise data

representative of a subject’s natural behaviour over extended

periods of time (e.g. an entire day or even a week) would be

Sebastian Madgwick is with the Department of Mechanical Engineering,

University of Bristol, e-mail: s.madgwick@bristol.ac.uk.

Ravi Vaidyanathan is with the Department of Mechanical Engineering, Uni-

versity of Bristol, Queens Building, BS8 1TR and the Department of Sys-

tems Engineering at the US Naval Postgraduate School, Monterey, CA, USA,

93940. e-mail: r.vaidyanathan@bristol.ac.uk.

Andrew Harrison is with the Department of Mechanical Engineering, Uni-

versity of Bristol, e-mail: andrew.j.l.harrison@bristol.ac.uk.

of signiﬁcant utility in this realm. In a recent survey, Zhoua

[7], cited real time operation, wireless properties, correctness

of data, and portability as major deﬁciencies that must be

addressed to realize a clinically viable system.

A. Inertial Motion Tracking Systems

Whilst a variety of technologies enable the measurement of

orientation, inertial based sensory systems have the advantage

of being completely self contained such that the measurement

entity is constrained neither in motion nor to any speciﬁc

environment or location. An IMU (Inertial Measurement Unit)

consists of gyroscopes and accelerometers enabling the track-

ing of rotational and translational movements. In order to

measure in three dimensions, tri-axis sensors consisting of 3

mutually orthogonal sensitive axes are required. A MARG

(Magnetic, Angular Rate, and Gravity) sensor is a hybrid

IMU which incorporates a tri-axis magnetometer. An IMU

alone can only measure an attitude relative to the direction of

gravity which is sufﬁcient for many applications [2], [1], [6].

MARG systems, also known as AHRS (Attitude and Heading

Reference Systems) are able to provide a complete measure-

ment of orientation relative to the direction of gravity and the

earth’s magnetic ﬁeld. An orientation estimation algorithm is

a fundamental component of any IMU or MARG system. It is

required to fuse together the separate sensor data into a single,

optimal estimate of orientation.

The Kalman ﬁlter [9] has become the accepted basis for

the majority of orientation algorithms [2], [10], [11], [12]

and commercial inertial orientation sensors; xsens [13], micro-

strain [14], VectorNav [15], Intersense [16], PNI [17] and

Crossbow [18] all produce systems founded on its use. The

widespread use of Kalman-based solutions are a testament

to their accuracy and effectiveness, however, they have a

number of disadvantages. They can be complicated to im-

plement which is reﬂected by the numerous solutions seen

in the subject literature [2], [10], [11], [12], [19], [20], [21],

[22], [23]. The linear regression iterations, fundamental to the

Kalman process, demand sampling rates which can far exceed

the subject bandwidth (e.g. a sampling rate between 512 Hz

[13] and 30 kHz [14] may be necessary for human motion

capture applications where system portability is critical). The

state relationships describing rotational kinematics in three-

dimensions typically require large state vectors and an ex-

tended Kalman ﬁlter implementation [2], [12], [19] to linearise

the problem.

These challenges demand a large computational load for

implementation of Kalman-based solutions and provide a clear

2011 IEEE International Conference on Rehabilitation Robotics

Rehab Week Zurich, ETH Zurich Science Cit

, Switzerland, June 29 - Jul

1, 2011

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