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1. Geometric extended state observer on TSE(3) with fast finite-time stability: Theory and validation on a multi-rotor vehicle

   https://doi.org/10.1016/j.ast.2024.109596  

   Wang, Ningshan; Hamrah, Reza; Sanyal, Amit K; Glauser, Mark N (December 2024, Aerospace Science and Technology)

   This article presents an extended state observer for a vehicle modeled as a rigid body in three-dimensional translational and rotational motions. The extended state observer is applicable to a multi-rotor aerial vehicle with a fixed plane of rotors, modeled as an under-actuated system on the state-space TSE(3), the tangent bundle of the six-dimensional Lie group SE(3). This state-space representation globally represents rigid body motions without singularities. The extended state observer is designed to estimate the resultant external disturbance force and disturbance torque acting on the vehicle. It guarantees stable convergence of disturbance estimation errors in finite time when the disturbances are constant, and finite time convergence to a bounded neighborhood of zero errors for time-varying disturbances. This extended state observer design is based on a Hölder-continuous fast finite time stable differentiator that is similar to the super-twisting algorithm, to obtain fast convergence. Numerical simulations are conducted to validate the proposed extended state observer. The proposed extended state observer is compared with other existing research to show its advantages. A set of experimental results implementing disturbance rejection control using feedback of disturbance estimates from this extended state observer is also presented. 

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2. 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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3. Adaptive Ankle Torque Control for Bipedal Humanoid Walking on Surfaces with Unknown Horizontal and Vertical Motion

   Stewart, Jacob; Chang, I-Chia; Gu, Yan; Ioannou, Petros A (July 2025, IEEE; American Control Conference)

   Achieving stable bipedal walking on surfaces with unknown motion remains a challenging control problem due to the hybrid, time-varying, partially unknown dynamics of the robot and the difficulty of accurate state and surface motion estimation. Surface motion imposes uncertainty on both system parameters and non-homogeneous disturbance in the walking robot dynamics. In this paper, we design an adaptive ankle torque controller to simultaneously address these two uncertainties and propose a step-length planner to minimize the required control torque. Typically, an adaptive controller is used for a continuous system. To apply adaptive control on a hybrid system such as a walking robot, an intermediate command profile is introduced to ensure a continuous error system. Simulations on a planar bipedal robot, along with comparisons against a baseline controller, demonstrate that the proposed approach effectively ensures stable walking and accurate tracking under unknown, time-varying disturbances. 

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4. Finite Time Stable Attitude and Angular Velocity Bias Estimation for Rigid Bodies With Unknown Dynamics

   https://doi.org/10.23919/ECC.2019.8796262  

   Sanyal, Amit K.; Warier, Rakesh R.; Hamrah, Reza (August 2019, 2019 18th European Control Conference (ECC))

   This paper presents a nonlinear finite-time stable attitude estimation scheme for a rigid body with unknown dynamics. Attitude is estimated from a minimum of two linearly independent known vectors measured in the body-fixed frame, and the angular velocity vector is assumed to have a constant bias in addition to measurement errors. Estimated attitude evolves directly on the special Euclidean group SO(3), avoiding any ambiguities. The constant bias in angular velocity measurements is also estimated. The estimation scheme is proven to be almost globally finite time stable in the absence of measurement errors using a Lyapunov analysis. For digital implementation, the estimation scheme is discretized as a geometric integrator. Numerical simulations demonstrate the robustness and convergence capabilities of the estimation scheme. 

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5. Control of a High Performance Bipedal Robot using Viscoelastic Liquid Cooled Actuators

   Junhyeok Ahn, Donghyun Kim (January 2019, IEEE International Conference on Humanoid Robots)

   This paper describes the control, and evaluation of a new human-scaled biped robot with liquid cooled viscoelastic actuators (VLCA). Based on the lessons learned from previous work from our team on VLCA, we present a new system design embodying a Reaction Force Sensing Series Elastic Actuator and a Force Sensing Series Elastic Actuator. These designs are aimed at reducing the size and weight of the robot’s actuation system while inheriting the advantages of our designs such as energy efficiency, torque density, impact resistance and position/force controllability. The robot design takes into consideration human-inspired kinematics and range-of-motion, while relying on foot placement to balance. In terms of actuator control, we perform a stability analysis on a Disturbance Observer designed for force control. We then evaluate various position control algorithms both in the time and frequency domains for our VLCA actuators. Having the low level baseline established, we first perform a controller evaluation on the legs using Operational Space Control. Finally, we move on to evaluating the full bipedal robot by accomplishing unsupported dynamic walking. 

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