The ever increasing need for performance results in increasingly rigorous demands on throughput and positioning accuracy of high-precision motion systems, which often suffer from position dependent effects that originate from relative actuation and sensing of the moving-body. Due to the highly stiff mechanical design, such systems are typically controlled using rigid body control design approaches. Nonetheless, the presence of position dependent flexible dynamics severely limits attainable position tracking performance. This paper presents two extensions of the conventional rigid body control framework towards active control of position dependent flexible dynamics. Additionally, a novel control design approach is presented, which allows for shaping of the full closed-loop system by means of structured $H_\infty$ co-design. The effectiveness of the approach is validated through simulation using a high-fidelity model of a state-of-the-art moving-magnet planar actuator.
Equivariance is a common and natural property of many nonlinear control systems, especially those associated with models of mechatronic and navigation systems. Such systems admit a symmetry, associated with the equivariance, that provides structure enabling the design of robust and high performance observers. A key insight is to pose the observer state to lie in the symmetry group rather than on the system state space. This allows one to define a globally defined intrinsic equivariant error but poses a challenge in defining internal dynamics for the observer. By choosing an equivariant lift of…
The rigid-body attitude tracking using vector and biased gyro measurements with unknown inertia matrix is studied in this note. First, a gyro-bias observer with global exponential stability is designed. Then, an attitude tracking controller based on this observer is devised, ensuring almost global asymptotic stability and almost semiglobal exponential stability. A separation property of the combined observer-controller is proved. Lastly, an adaptive attitude tracking controller relying on a modified gyro-bias observer and with no over-parametrization is developed to deal with the unknown inert…
This report proposes a discrete time observer for the continuous time rigid body kinematics on the rotation group $\mathbb{S}\mathbb{O}(3)$. The work draws on two research schools - one by Chang based on feedback integrators for systems evolving on manifolds,and the other by Mahony, who proposed an observer for attitude dynamics. The discrete time observer is based on the modified dynamics of the Mahony observer for attitude dynamics, where the modification of the vector field enables numerical integration based on Euclidean schemes.
The problem of estimating the angular speed of a solid body from attitude measurements is addressed. To solve this problem, we propose an observer whose dynamics are not constrained to evolve on any specific manifold. This drastically simplifies the analysis of the proposed observer. Using Lyapunov analysis, sufficient conditions for global asymptotic stability of a set wherein the estimation error is equal to zero are established. In addition, the proposed methodology is adapted to deal with angular speed estimation for systems evolving on the unit circle. The approach is illustrated through …
The paper addresses the problem of attitude estimation for rigid bodies using (possibly time-varying) vector measurements, for which we provide a necessary and sufficient condition of distinguishability. Such a condition is shown to be strictly weaker than those previously used for attitude observer design. Thereafter, we show that even for the single vector case the resulting condition is sufficient to design almost globally convergent attitude observers, and two explicit designs are obtained. To overcome the weak excitation issue, the first design employs to make full use of historical infor…
Successful navigation of a rigid-body traveling with six degrees of freedom (6 DoF) requires accurate estimation of attitude , position, and linear velocity. The true navigation dynamics are highly nonlinear and are modeled on the matrix Lie group of SE2(3). This paper presents novel geometric nonlinear continuous stochastic navigation observers on SE2(3) capturing the true nonlinearity of the problem. The proposed observers combines IMU and landmark measurements. It efficiently handles the IMU measurement noise. The proposed observers are guaranteed to be almost semi-globally uniformly ultima…
A General Nonlinear Observer Design for Inertial Navigation Systems with Almost Global Stability Guarantees
Capgemini Engineering（凯捷工程）；University of Quebec in Outaouais（渥太华大学）；I3S-UniCA-CNRS, University Cote d’Azur（尼斯大学）；Institut Universitaire de France（法国高等研究院）
Western University（韦仕敦大学）；Lakehead University（湖首大学）
This paper considers the problem of attitude, position and linear velocity estimation for rigid body systems relying on landmark measurements. We propose two hybrid nonlinear observers on the matrix Lie group $SE_2(3)$, leading to global exponential stability. The first observer relies on fixed gains, while the second one uses variable gains depending on the solution of a continuous Riccati equation (CRE). These observers are then extended to handle biased angular velocity measurements. Both simulation and experimental results are presented to illustrate the performance of the proposed observe…
In this paper, we incorporate velocity observer design into the virtual decomposition control (VDC) strategy of an $n$-DoF open chain robotic manipulator. Descending from the VDC strategy, the proposed design is based on decomposing the $n$-DoF manipulator into subsystems, i.e., rigid links and joints, for which the decentralized controller-observer implementation can be done locally. Similar to VDC, the combined controller-observer design is passivity-based, and we show that it achieves semiglobal exponential convergence of the tracking error. The convergence analysis is carried out using Lya…
Growing demands in the semiconductor industry result in the need for enhanced performance of lithographic equipment. However, position tracking accuracy of high precision mechatronics is often limited by the presence of disturbance sources, which originate from unmodelled or unforeseen deterministic environmental effects. To negate the effects of these disturbances, a learning based feedforward controller is employed, where the underlying control policy is estimated from experimental data based on Gaussian Process regression. The proposed approach exploits the property of including prior knowl…
The position and the orientation of a rigid body object pushed by a robot on a planar surface are extremely difficult to predict. In this paper, the prediction problem is formulated as a disturbance observer design problem. The disturbance observer provides accurate estimation of the total sum of model errors and external disturbances acting on the object. From the estimation results, it is revealed that there is a strong linear relationship between the applied force or torque and the estimated disturbances. The proposed prediction algorithm has two phases: the identification & the prediction.…
Cascaded Tightly-Coupled Observer Design for Single-Range-Aided Inertial Navigation
Department of Computer Science（计算机科学系）；Engineering, University of Quebec in Outaouais, Gatineau, QC, Canada（魁北克大学Outaouais工程学院，加蒂纳岛，QC，加拿大）；Department of Electrical and Computer Engineering（电气与计算机工程系）；Lakehead University（拉克头大学）
Pose, Velocity and Landmark Position Estimation Using IMU and Bearing Measurements
School of Artificial Intelligence and Automation, Huazhong University of Science and Technology（华中科技大学人工智能与自动化学院）；Department of Electrical Engineering, Lakehead University（湖首大学电气工程系）；Department of Electrical and Computer Engineering, Western University（西安大略大学电气与计算机工程系）
