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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. Data-Driven Decomposition Control to Output Tracking With Nonperiodic Tracking–Transition Switching Under Input Constraint

   https://doi.org/10.1115/1.4053763  

   Liu, Jiangbo ; Zou, Qingze ( June 2022 , Journal of Dynamic Systems, Measurement, and Control)

   Abstract This paper is concerned with solving, from the learning-based decomposition control viewpoint, the problem of output tracking with nonperiodic tracking–transition switching. Such a nontraditional tracking problem occurs in applications where sessions for tracking a given desired trajectory are alternated with those for transiting the output with given boundary conditions. It is challenging to achieve precision tracking while maintaining smooth tracking–transition switching, as postswitching oscillations can be induced due to the mismatch of the boundary states at the switching instants, and the tracking performance can be limited by the nonminimum-phase (NMP) zeros of the system and effected by factors such as input constraints and external disturbances. Although recently an approach by combining the system-inversion with optimization techniques has been proposed to tackle these challenges, modeling of the system dynamics and complicated online computation are needed, and the controller obtained can be sensitive to model uncertainties. In this work, a learning-based decomposition control technique is developed to overcome these limitations. A dictionary of input–output bases is constructed offline a priori via data-driven iterative learning first. The input–output bases are used online to decompose the desired output in the tracking sessions and design an optimal desired transition trajectory with minimal transition time under input-amplitude constraint. Finally, the control input is synthesized based on the superpositioning principle and further optimized online to account for system variations and external disturbance. The proposed approach is illustrated through a nanopositioning control experiment on a piezoelectric actuator. 

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4. 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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5. Adaptive formation control architectures for a team of quadrotors with multiple performance and safety constraints

   https://doi.org/10.1002/rnc.6824  

   Hu, Zhongjun ; Jin, Xu ( September 2023 , International Journal of Robust and Nonlinear Control)

   In this work, we propose a novel adaptive formation control architecture for a group of quadrotor systems, under line‐of‐sight (LOS) distance and relative distance constraints as well as attitude constraints, where the constraint requirements can be both asymmetric and time‐varying in nature. The LOS distance constraint consideration ensures that each quadrotor is not deviating too far away from its desired flight trajectory. The LOS relative inter‐quadrotor distance constraint is to guarantee that the LOS distance between any two quadrotors in the formation is neither too large (which may result in the loss of communication between quadrotors, for example) nor too small (which may result in collision between quadrotors, for example). The attitude constraints make sure that the roll, pitch, and yaw angles of each quadrotor do not deviate too much from the desired profile. Universal barrier functions are adopted in the controller design and analysis, which is a generic framework that can address system with different types of constraints in a unified controller architecture. Furthermore, each quadrotor's mass and inertia are unknown, and the system dynamics are subjected to time‐varying external disturbances. Through rigorous analysis, an exponential convergence rate can be guaranteed on the distance and attitude tracking errors, while all constraints are satisfied during the operation. A simulation example further demonstrates the efficacy of the proposed control framework.

    

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