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1. Finite-time stable disturbance observer for unmanned aerial vehicles

   https://doi.org/10.23919/ACC53348.2022.9867308  

   Bhale, Pradhyumn; Kumar, Mrinal; Sanyal, Amit K. (June 2022, 2022 American Control Conference (ACC))

   This work provides a finite-time stable disturbance observer design for the discretized dynamics of an unmanned vehicle in three-dimensional translational and rotational motion. The dynamics of this vehicle is discretized using a Lie group variational integrator as a grey box dynamics model that also accounts for unknown additive disturbance force and torque. Therefore, the input-state dynamics is partly known. The unknown dynamics is lumped into a single disturbance force and a single disturbance torque, both of which are estimated using the disturbance observer we design. This disturbance observer is finite-time stable (FTS) and works like a real-time machine learning scheme for the unknown dynamics. 

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2. A Finite-Time Stable Observer for Relative Attitude Estimation

   https://doi.org/10.1109/CDC40024.2019.9029806  

   Wang, Ningshan; Hamrah, Reza; Sanyal, Amit K. (December 2019, 2019 IEEE 58th Conference on Decision and Control (CDC))

   Relative motion estimation of one rigid body with respect to another is a problem that has immediate applications to formations and maneuvers involving multiple unmanned vehicles or collision avoidance between vehicles. A finite-time stable observer for relative attitude estimation of a rigid object using onboard sensors on an unmanned vehicle, is developed and presented here. This observer assumes sensor inputs from onboard vision and inertial sensors, with the vision sensors measuring at least three points on the object whose relative locations with respect to a body-fixed frame on the object are also assumed to be known. In the absence of any measurement noise, the estimated relative attitude is shown to converge to the actual relative pose in a finite-time stable manner. Numerical simulations indicate that this relative attitude observer is robust to persistent measurement errors and converges to a bounded neighborhood of the true attitude. 

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3. Variational Observer Designs on Lie Groups, with Applications to Rigid Body Motion Estimation

   https://doi.org/10.1109/CDC56724.2024.10886160  

   Srinivasu, Neon; Dongare, Abhijit; Sanyal, Amit K (December 2024, IEEE)

   Variational estimation of a mechanical system is based on the application of variational principles from mechanics to state estimation of the system evolving on its configuration manifold. If the configuration manifold is a Lie group, then the underlying group structure can be used to design nonlinearly stable observers for estimation of configuration and velocity states from measurements. Measured quantities are on a vector space on which the Lie group acts smoothly. We formulate the design of variational observers on a general finite-dimensional Lie group, followed by the design and experimental evaluation of a variational observer for rigid body motions on the Lie group SE(3). 

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4. Invariant Extended Kalman Filtering for Human Motion Estimation with Imperfect Sensor Placement

   https://doi.org/10.23919/ACC53348.2022.9867745  

   Zhu, Zenan; Rezayat Sorkhabadi, Seyed Mostafa; Gu, Yan; Zhang, Wenlong (June 2022, American Control Conference)

   This paper introduces a new invariant extended Kalman filter design that produces real-time state estimates and rapid error convergence for the estimation of the human body movement even in the presence of sensor misalignment and initial state estimation errors. The filter fuses the data returned by an inertial measurement unit (IMU) attached to the body (e.g., pelvis or chest) and a virtual measurement of zero stance-foot velocity (i.e., leg odometry). The key novelty of the proposed filter lies in that its process model meets the group affine property while the filter explicitly addresses the IMU placement error by formulating its stochastic process model as Brownian motions and incorporating the error in the leg odometry. Although the measurement model is imperfect (i.e., it does not possess an invariant observation form) and thus its linearization relies on the state estimate, experimental results demonstrate fast convergence of the proposed filter (within 0.2 seconds) during squatting motions even under significant IMU placement inaccuracy and initial estimation errors. 

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5. A Hölder-continuous Extended State Observer for Model-free Position Tracking Control

   https://doi.org/10.23919/ACC50511.2021.9483268  

   Wang, Ningshan; Sanyal, Amit K. (May 2021, 2021 American Control Conference (ACC))

   null (Ed.)

   Position tracking control in three spatial dimensions in the presence of unknown or uncertain dynamics, is applicable to unmanned aerial, ground, (under)water and space vehicles. This work gives a new approach to model-free position tracking control by designing an extended state observer to estimate the states and the uncertain dynamics, with guaranteed accuracy of estimates. The estimated states and uncertainties can be used in a control scheme in real-time for position tracking control. The uncertainty (disturbance input) estimate is provided by an extended state observer (ESO) that is finite-time stable (FTS), to provide accuracy and robustness. The ideas of homogeneous vector fields and real-valued functions are utilized for the ESO design and to prove FTS. The estimated disturbance is then utilized for compensation of this uncertainty in real-time, and to enhance the stability and robustness of the feedback tracking control scheme. 

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