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1. Hybrid Hierarchical Statistical Control of Robotic Manipulators

   Lash, Steven; Saleheen, Firdous; Won, Chang-hee (March 2022, SICE International Symposium on Control Systems)

   Here we present a hybrid hierarchical statistical control approach for the control of robotic manipulators. The bimodal dynamic imaging system considered in this paper utilizes two robotic manipulators to move the source and detector imaging modules. As this system contains both continuous and discrete dynamics, hybrid system control techniques are applied. The robotic arms used in this research are comprised of compliant joints, which have been shown to introduce process noise into the system. To address this, a full-state feedback statistical controller is developed to minimize joint angle variations for the system. The statistical controllers for the two robot arms are then coordinated using a hierarchical controller. Finally, the feasibility of the hybrid hierarchical statistical controller is demonstrated with numerical simulations. 

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2. 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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3. Hybrid FES-exoskeleton control: Using MPC to distribute actuation for elbow and wrist movements

   https://doi.org/10.3389/fnbot.2023.1127783  

   Dunkelberger, Nathan; Berning, Jeffrey; Schearer, Eric M.; O'Malley, Marcia K. (April 2023, Frontiers in Neurorobotics)

   IntroductionIndividuals who have suffered a cervical spinal cord injury prioritize the recovery of upper limb function for completing activities of daily living. Hybrid FES-exoskeleton systems have the potential to assist this population by providing a portable, powered, and wearable device; however, realization of this combination of technologies has been challenging. In particular, it has been difficult to show generalizability across motions, and to define optimal distribution of actuation, given the complex nature of the combined dynamic system. MethodsIn this paper, we present a hybrid controller using a model predictive control (MPC) formulation that combines the actuation of both an exoskeleton and an FES system. The MPC cost function is designed to distribute actuation on a single degree of freedom to favor FES control effort, reducing exoskeleton power consumption, while ensuring smooth movements along different trajectories. Our controller was tested with nine able-bodied participants using FES surface stimulation paired with an upper limb powered exoskeleton. The hybrid controller was compared to an exoskeleton alone controller, and we measured trajectory error and torque while moving the participant through two elbow flexion/extension trajectories, and separately through two wrist flexion/extension trajectories. ResultsThe MPC-based hybrid controller showed a reduction in sum of squared torques by an average of 48.7 and 57.9% on the elbow flexion/extension and wrist flexion/extension joints respectively, with only small differences in tracking accuracy compared to the exoskeleton alone. DiscussionTo realize practical implementation of hybrid FES-exoskeleton systems, the control strategy requires translation to multi-DOF movements, achieving more consistent improvement across participants, and balancing control to more fully leverage the muscles' capabilities. 

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4. A hybrid feedback control strategy for autonomous waypoint transitioning and loitering of unmanned aerial vehicles

   Smith, Dean A; Sanfelice, Ricardo G (November 2017, Nonlinear analysis. Hybrid systems)

   We consider the problem of autonomously controlling a fixed-wing aerial vehicle to visit a neighborhood of a pre-defined waypoint, and when nearby it, loiter around it. To solve this problem, we propose a hybrid feedback control strategy that unites two state-feedback controllers: a transit controller capable of steering or transitioning the vehicle to nearby the waypoint and a loiter controller capable of steering the vehicle about a loitering radius. The aerial vehicle is modeled on a level flight plane with system performance characterized in terms of the aerodynamic, propulsion, and mass properties. Thrust and bank angle are the control inputs. Asymptotic stability properties of the individual control algorithms, which are designed using backstepping, as well as of the closed-loop system, which includes a hybrid algorithm uniting the two controllers, are established. In particular, for this application of hybrid feedback control, Lyapunov functions and hybrid systems theory are employed to establish stability properties of the set of points defining loitering. The analytical results are confirmed numerically by simulations. 

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5. Design of smooth hybrid controllers for a class of non‐linear systems

   https://doi.org/10.1049/iet-cta.2019.1112  

   Shamgah, Laya; Getahun_Tadewos, Tadewos; Karimoddini, Ali (February 2021, IET Control Theory & Applications)

   Symbolic planning techniques rely on abstract information about a continuous system to design a discrete planner to satisfy desired high‐level objectives. However, applying the generated discrete commands of the discrete planner to the original system may face several challenges, including real‐time implementation, preserving the properties of high‐level objectives in the continuous domain, and issues such as discontinuity in control signals that may physically harm the system. To address these issues and challenges, the authors proposed a novel hybrid control structure for systems with non‐linear multi‐affine dynamics over rectangular partitions. In the proposed framework, a discrete planner can be separately designed to achieve high‐level specifications. Then, the proposed hybrid controller generates jumpless continuous control signals to drive the system over the partitioned space executing the discrete commands of the planner. The hybrid controller generates continuous signals in real‐time while respecting the dynamics of the system and preserving the desired objectives of the high‐level plan. The design process is described in detail and the existence and uniqueness of the proposed solution are investigated. Finally, several case studies are provided to verify the effectiveness of the developed technique. 

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