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 magnetic 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.

Estimation of IMU and MARG orientation using a gradient descent algorithm

This paper considers the problem of obtaining good attitude estimates from measurements obtained from typical low cost inertial measurement units. The outputs of such systems are characterized by high noise levels and time varying additive biases. We formulate the filtering problem as deterministic observer kinematics posed directly on the special orthogonal group SO (3) driven by reconstructed attitude and angular velocity measurements. Lyapunov analysis results for the proposed observers are derived that ensure almost global stability of the observer error. The approach taken leads to an observer that we term the direct complementary filter. By exploiting the geometry of the special orthogonal group a related observer, termed the passive complementary filter, is derived that decouples the gyro measurements from the reconstructed attitude in the observer inputs. Both the direct and passive filters can be extended to estimate gyro bias online. The passive filter is further developed to provide a formulation in terms of the measurement error that avoids any algebraic reconstruction of the attitude. This leads to an observer on SO(3), termed the explicit complementary filter, that requires only accelerometer and gyro outputs; is suitable for implementation on embedded hardware; and provides good attitude estimates as well as estimating the gyro biases online. The performance of the observers are demonstrated with a set of experiments performed on a robotic test-bed and a radio controlled unmanned aerial vehicle.

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Nonlinear Complementary Filters on the Special Orthogonal Group

There has been increased research interest in systems composed of multiple autonomous mobile robots exhibiting cooperative behavior. Groups of mobile robots are constructed, with an aim to studying such issues as group architecture, resource conflict, origin of cooperation, learning, and geometric problems. As yet, few applications of cooperative robotics have been reported, and supporting theory is still in its formative stages. In this paper, we give a critical survey of existing works and discuss open problems in this field, emphasizing the various theoretical issues that arise in the study of cooperative robotics. We describe the intellectual heritages that have guided early research, as well as possible additions to the set of existing motivations.

Cooperative mobile robotics: antecedents and directions

Provides a summary of recent developments in control of nonholonomic systems. The published literature has grown enormously during the last six years, and it is now possible to give a tutorial presentation of many of these developments. The objective of this article is to provide a unified and accessible presentation, placing the various models, problem formulations, approaches, and results into a proper context. It is hoped that this overview will provide a good introduction to the subject for nonspecialists in the field, while perhaps providing specialists with a better perspective of the field as a whole. The paper is organized as follows: introduction to nonholonomic control systems and where they arise in applications, classification of models of nonholonomic control systems, control problem formulations, motion planning results, stabilization results, and current and future research topics.

Developments in nonholonomic control problems

In this paper, we survey the field of robotic grasping and the work that has been done in this area over the last two decades, with a slight bias toward the development of the theoretical framework and analytical results in this area.

Robotic grasping and contact: a review

Presents an extended Kalman filter for real-time estimation of rigid body orientation using the newly developed MARG (magnetic, angular rate, and gravity) sensors. Each MARG sensor contains a three-axis magnetometer, a three-axis angular rate sensor, and a three-axis accelerometer. The filter represents rotations using quaternions rather than Euler angles, which eliminates the long-standing problem of singularities associated with attitude estimation. A process model for rigid body angular motions and angular rate measurements is defined. The process model converts angular rates into quaternion rates, which are integrated to obtain quaternions. The Gauss-Newton iteration algorithm is utilized to find the best quaternion that relates the measured accelerations and earth magnetic field in the body coordinate frame to calculated values in the earth coordinate frame. The best quaternion is used as part of the measurements for the Kalman filter. As a result of this approach, the measurement equations of the Kalman filter become linear, and the computational requirements are significantly reduced, making it possible to estimate orientation in real time. Extensive testing of the filter with synthetic data and actual sensor data proved it to be satisfactory. Test cases included the presence of large initial errors as well as high noise levels. In all cases the filter was able to converge and accurately track rotational motions.

An extended Kalman filter for quaternion-based orientation estimation using MARG sensors

Real-time tracking of human body motion is an important technology in synthetic environments, robotics, and other human-computer interaction applications. This paper presents an extended Kalman filter designed for real-time estimation of the orientation of human limb segments. The filter processes data from small inertial/magnetic sensor modules containing triaxial angular rate sensors, accelerometers, and magnetometers. The filter represents rotation using quaternions rather than Euler angles or axis/angle pairs. Preprocessing of the acceleration and magnetometer measurements using the Quest algorithm produces a computed quaternion input for the filter. This preprocessing reduces the dimension of the state vector and makes the measurement equations linear. Real-time implementation and testing results of the quaternion-based Kalman filter are presented. Experimental results validate the filter design, and show the feasibility of using inertial/magnetic sensor modules for real-time human body motion tracking

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Design, Implementation, and Experimental Results of a Quaternion-Based Kalman Filter for Human Body Motion Tracking

A mobile manipulator in this study is a manipulator mounted on a mobile platform. Assuming the end point of the manipulator is guided, e.g., by a human operator to follow an arbitrary trajectory, it is desirable that the mobile platform is able to move as to position the manipulator in certain preferred configurations. Since the motion of the manipulator is unknown a priori, the platform has to use the measured joint position information of the manipulator for its own motion planning. This paper presents a control algorithm for the platform so that the manipulator is always positioned at the preferred configurations measured by its manipulability. Simulation results are presented to illustrate the efficacy of the algorithm. The algorithm is also implemented and verified on a real mobile manipulator system. The use of the resulting algorithm in a number of applications is also discussed. >

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Coordinating locomotion and manipulation of a mobile manipulator

There are many examples of mechanical systems that require rolling contacts between two or more rigid bodies. Rolling contacts engender nonholonomic constraints in an otherwise holonomic system. In this article, we develop a unified approach to the control of mechanical systems subject to both holonomic and nonholonomic constraints. We first present a state space realization of a constrained system. We then discuss the input-output linearization and zero dynamics of the system. This approach is applied to the dynamic control of mobile robots. Two types of control algorithms for mobile robots are investigated: trajectory tracking and path following. In each case, a smooth nonlinear feedback is obtained to achieve asymptotic input-output stability and Lagrange stability of the overall system. Simulation results are presented to demonstrate the effectiveness of the control algorithms and to compare the performane of trajectory-tracking and path-following algorithms.

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Control of Mechanical Systems With Rolling Constraints: Application to Dynamic Control of Mobile Robots

A planning and control algorithm for coordinating the motion of a mobile manipulator is presented. The design criterion is to control the mobile platform so that the manipulator is maintained in a configuration which maximizes the manipulability measure. The effectiveness of the method was verified by simulations on two representative trajectories. The algorithm was implemented with an actual mobile manipulator and tested on one of the trajectories for comparison purposes. >

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Xiaoping Yun

Papers

An extended Kalman filter for quaternion-based orientation estimation using MARG sensors

Design, Implementation, and Experimental Results of a Quaternion-Based Kalman Filter for Human Body Motion Tracking

Coordinating locomotion and manipulation of a mobile manipulator

Control of Mechanical Systems With Rolling Constraints: Application to Dynamic Control of Mobile Robots

Coordinating locomotion and manipulation of a mobile manipulator