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1. Experimental and Analytical Prescribed-Time Trajectory Tracking Control of a 7-DOF Robot Manipulator

   https://doi.org/10.23919/ACC53348.2022.9867788  

   Bertino, Alexander ; Naseradinmousavi, Peiman ; Krstic, Miroslav ( June 2022 , American Control Conference (ACC))

   We present an analytical design and experimental verification of trajectory tracking control of a 7-DOF robot manipulator, which achieves convergence of all tracking errors to the origin within a finite terminal time. A key feature of this control strategy is that this terminal convergence time is explicitly prescribed by the control designer, and is thus independent of the initial conditions of the tracking errors. In order to achieve this beneficial property of the proposed controller, a scaling of the state by a function of time that grows unbounded towards the terminal time is employed. Through Lyapunov analysis, we first demonstrate that the proposed controller achieves regulation of all tracking errors within the prescribed time as well as the uniform boundedness of the joint torques, even in the presence of a matched, non-vanishing disturbance. Then, through both simulation and experiment, we demonstrate that the proposed controller is capable of converging to the desired trajectory within the prescribed time, despite large initial conditions of the tracking errors and a sinusoidal disturbance being applied in each joint. 

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2. A Hybrid Predictive Control Approach to Trajectory Tracking for a Fully Actuated Biped

   https://doi.org/10.23919/ACC.2018.8431254  

   Short, Brendan E. ; Sanfelice, Ricardo G. ( June 2018 , 2018 Annual American Control Conference (ACC))

   We model a three-link fully actuated biped as a hybrid system and propose a prediction-based control algorithm for global tracking of reference trajectories. The proposed control strategy consists of a reference system that generates the desired periodic gait, a virtual system that generates a suitable reference trajectory using prediction, and a tracking control law that steers the biped to the virtual trajectory. The proposed algorithms achieves, in finite time, tracking in two steps. We present mathematical properties that define the main elements in the hybrid predictive controller for achieving convergence to the reference within the first two steps. The results are validated through numerical simulations. 

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3. Global-Position Tracking Control for Three-Dimensional Bipedal Robots Via Virtual Constraint Design and Multiple Lyapunov Analysis

   https://doi.org/10.1115/1.4054732  

   Gu, Yan ; Gao, Yuan ; Yao, Bin ; Lee, C. S. ( November 2022 , Journal of Dynamic Systems, Measurement, and Control)

   Abstract A safety-critical measure of legged locomotion performance is a robot's ability to track its desired time-varying position trajectory in an environment, which is herein termed as “global-position tracking.” This paper introduces a nonlinear control approach that achieves asymptotic global-position tracking for three-dimensional (3D) bipedal robots. Designing a global-position tracking controller presents a challenging problem due to the complex hybrid robot model and the time-varying desired global-position trajectory. Toward tackling this problem, the first main contribution is the construction of impact invariance to ensure all desired trajectories respect the foot-landing impact dynamics, which is a necessary condition for realizing asymptotic tracking of hybrid walking systems. Thanks to their independence of the desired global position, these conditions can be exploited to decouple the higher-level planning of the global position and the lower-level planning of the remaining trajectories, thereby greatly alleviating the computational burden of motion planning. The second main contribution is the Lyapunov-based stability analysis of the hybrid closed-loop system, which produces sufficient conditions to guide the controller design for achieving asymptotic global-position tracking during fully actuated walking. Simulations and experiments on a 3D bipedal robot with twenty revolute joints confirm the validity of the proposed control approach in guaranteeing accurate tracking. 

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4. Hierarchical MPC with Coordinating Terminal Costs

   https://doi.org/10.23919/ACC45564.2020.9147685  

   Raghuraman, Vignesh ; Renganathan, Venkatraman ; Summers, Tyler H. ; Koeln, Justin P. ( July 2020 , American Control Conference)

   null (Ed.)

   The performance of hierarchical Model Predictive Control (MPC) is highly dependent on the mechanisms used to coordinate the decisions made by controllers at different levels of the hierarchy. Conventionally, reference tracking serves as the primary coordination mechanism, where optimal state and input trajectories determined by upper-level controllers are communicated down the hierarchy to be tracked by lower-level controllers. As such, significant tuning is required for each controller in the hierarchy to achieve the desired closed-loop system performance. This paper presents a novel terminal cost coordination mechanism using constrained zonotopes, designed to improve system performance under hierarchical control. These terminal costs allow lower-level controllers to balance both short- and long-term control performance without the need for controller tuning. Unlike terminal costs widely used to guarantee MPC stability, the proposed terminal costs are time-varying and computed on-line based on the optimal state trajectory of the upper-level controllers. A numerical example demonstrates the provable performance benefits achieved using the proposed terminal cost coordination mechanism. 

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5. A High-Gain Observer Approach to Robust Trajectory Estimation and Tracking for a Multirotor Unmanned Aerial Vehicle

   https://doi.org/10.1115/1.4065758  

   Boss, Connor J ; Srivastava, Vaibhav ( January 2025 , Journal of Dynamic Systems, Measurement, and Control)

   Using the context of trajectory estimation and tracking for multirotor unmanned aerial vehicles (UAVs), we explore the challenges in applying high-gain observers to highly dynamic systems. The multirotor will operate in the presence of external disturbances and modeling errors. At the same time, the reference trajectory is unknown and generated from a reference system with unknown or partially known dynamics. We assume the only measurements that are available are the position and orientation of the multirotor and the position of the reference system. We adopt an extended high-gain observer (EHGO) estimation framework to estimate the unmeasured multirotor states, modeling errors, external disturbances, and the reference trajectory. We design a robust output feedback controller for trajectory tracking that comprises a feedback linearizing controller and the EHGO. The proposed control method is rigorously analyzed to establish its stability properties. Finally, we illustrate our theoretical results through numerical simulation and experimental validation in which a multirotor tracks a moving ground vehicle with an unknown trajectory and dynamics and successfully lands on the vehicle while in motion.

    

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