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1. Verifying Switched System Stability With Logic

   https://doi.org/10.1145/3501710.3519541  

   Tan, Yong Kiam; Mitsch, Stefan; Platzer, André (May 2022, Hybrid Systems: Computation and Control (part of CPS Week 2022), HSCC'22)

   Bartocci, Ezio; Putot, Sylvie (Ed.)

   Switched systems are known to exhibit subtle (in)stability behaviors requiring system designers to carefully analyze the stability of closed-loop systems that arise from their proposed switching control laws. This paper presents a formal approach for verifying switched system stability that blends classical ideas from the controls and verification literature using differential dynamic logic (dL), a logic for deductive verification of hybrid systems. From controls, we use standard stability notions for various classes of switching mechanisms and their corresponding Lyapunov function-based analysis techniques. From verification, we use dL's ability to verify quantified properties of hybrid systems and dL models of switched systems as looping hybrid programs whose stability can be formally specified and proven by finding appropriate loop invariants, i.e., properties that are preserved across each loop iteration. This blend of ideas enables a trustworthy implementation of switched system stability verification in the KeYmaera X prover based on dL. For standard classes of switching mechanisms, the implementation provides fully automated stability proofs, including searching for suitable Lyapunov functions. Moreover, the generality of the deductive approach also enables verification of switching control laws that require non-standard stability arguments through the design of loop invariants that suitably express specific intuitions behind those control laws. This flexibility is demonstrated on three case studies: a model for longitudinal flight control by Branicky, an automatic cruise controller, and Brockett's nonholonomic integrator. 

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2. Dynamic Modeling and Robust Torque Control of a Discrete Variable Stiffness Actuator

   https://doi.org/10.1115/DETC2023-115235  

   Yu, Ziqing; Fu, Jiaming; Yao, Bin; Chiu, George; Voyles, Richard; Gan, Dongming (August 2023, American Society of Mechanical Engineers)

   Abstract Collaborative robots, or cobots, have been developed as a solution to the growing need for robots that can work alongside humans safely and effectively. One emerging technology in robotics is the use of Discrete Variable Stiffness Actuators (DVSAs), which enable robots to adjust their stiffness in a fast-discrete manner. This enables cobots to work in both low and high stiffness modes, allowing for safe collaboration with human workers or operation behind safety barriers. However, achieving good performance with different stiffness modes of DVSAs is a challenging problem. This paper proposes a method to provide force control of a DVSA by exploiting the dynamic model and the discrete stiffness levels. The two-mass dynamic model, a widely accepted model of flexible systems, is used to model and analyze the DVSA. The proposed method involves using Gain-scheduling and Deterministic Robust Control (DRC) controllers as modelbased control algorithms for the DVSA to achieve high-precision force control. We also conducted a comparison with the commonly used proportional integral derivative (PID) control algorithms. The paper presents a detailed analysis of the dynamic behavior of the DVSA and demonstrates the effectiveness of the proposed control algorithms through simulation with different scenario comparisons, even in the presence of external disturbances. 

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3. Model reference adaptive anti-windup compensation

   https://doi.org/10.1109/CDC51059.2022.9992768  

   Sofrony, Jorge; Turner, Matthew; Richards, Christopher (December 2022, IEEE)

   This paper proposes an anti-windup mechanism for a model reference adaptive control scheme subject to actuator saturation constraints. The proposed compensator has the same architecture as well known non-adaptive schemes, which rely on the assumption that the system model is known fairly accurately. This is in contrast to the adaptive nature of the controller, which assumes that the system (or parts of it) is unknown. The approach proposed here uses of an “estimate” of the system matrices for the anti-windup compensator formulation and modifies the adaptation laws that update the controller gains. It will be observed that if the (unknown) ideal control gain is reached, a type of “model recovery anti-windup” formulation is obtained. In addition, it is shown that if the ideal control signal eventually lies within the control constraints, then, under certain conditions, the system states will converge to those of the reference model as desired. The paper highlights the main challenges involved in the design of anti-windup compensators for model-reference adaptive control systems and demonstrates its success via a flight control simulation. 

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4. Model Evolutionary Gain-Based Predictive Control (MEGa-PC) for Soft Robotics*

   https://doi.org/10.1109/RoboSoft60065.2024.10521954  

   Jensen, Spencer; Salmon, John L; Killpack, Marc D (April 2024, IEEE)

   This paper details a reliable control method for highly nonlinear dynamical systems such as soft robots. We call this method model evolutionary gain-based predictive control or MEGa-PC. The method uses an evolutionary algorithm to optimize a set of controller gains via model predictive control. We demonstrate the performance of MEGa-PC in simulation for a single-link inverted pendulum and a threelink inverted pendulum, and on physical hardware for a threejoint continuum soft robot arm with six degrees of freedom. MEGa-PC is compared to prior work that used Nonlinear Evolutionary Model Predictive Control or NEMPC. The new method performs similarly to NEMPC in terms of accumulated cost over the entire trajectory, however, MEGa-PC generalizes better to real-world applications where safety is paramount, the dynamic model is uncertain, the system has significant latency, and where the previous sampling-based method (NEMPC) resulted in significant steady-state error due to model inaccuracy. 

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5. Motion planning under uncertainty and sensing limitations using exploration versus exploitation

   Saumya Saxena, Matthew Travers (October 2019, SUBMITTED to the IEEE Intelligent Robot Systems)

   We consider a planning problem for a robot operating in an information-degraded environment. Our contribution to the state of the art is addressing this problem when robots have limited sensing capabilities, and thus only acquire information in certain locations. We therefore need a method that balances between driving the robot to the goal and toward regions to gain information (or to reduce uncertainty). We present a novel sampling-based planner (Particle Filter based Affine Quadratic Tree --- PF-AQT) that explores the environment, and plans to reach a goal with minimal uncertainty. We then use the output trajectory from PF-AQT to initialize an optimization-based planner that finds a locally optimal trajectory that minimizes control effort and uncertainty. In doing so we reap the exploration benefits of sampling-based methods and exploitation benefits of optimization-based methods for dealing with uncertainty and limited sensing capabilities of the robot. We demonstrate our results using two dynamical systems: double integrator model and a non-holonomic car-like robot. 

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