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1. A Simple Controller for Omnidirectional Trotting of Quadrupedal Robots: Command Following and Waypoint Tracking

   https://doi.org/10.3390/robotics12020035  

   Bhounsule, Pranav A.; Yang, Chun-Ming (April 2023, Robotics)

   For autonomous legged robots to be deployed in practical scenarios, they need to perform perception, motion planning, and locomotion control. Since robots have limited computing capabilities, it is important to realize locomotion control with simple controllers that have modest calculations. The goal of this paper is to create computational simple controllers for locomotion control that can free up computational resources for more demanding computational tasks, such as perception and motion planning. The controller consists of a leg scheduler for sequencing a trot gait with a fixed step time; a reference trajectory generator for the feet in the Cartesian space, which is then mapped to the joint space using an analytical inverse; and a joint controller using a combination of feedforward torques based on static equilibrium and feedback torque. The resulting controller enables velocity command following in the forward, sideways, and turning directions. With these three velocity command following-modes, a waypoint tracking controller is developed that can track a curve in global coordinates using feedback linearization. The command following and waypoint tracking controllers are demonstrated in simulation and on hardware. 

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2. Hybrid Event Shaping to Stabilize Periodic Hybrid Orbits

   Zhu, James; Kong, Nathan J.; Council, George; Johnson, Aaron M. (May 2022, IEEE International Conference on Robotics and Automation)

   Many controllers for legged robotic systems leverage open- or closed-loop control at discrete hybrid events to enhance stability. These controllers appear in several well studied phenomena such as the Raibert stepping controller, paddle juggling, and swing leg retraction. This work introduces hybrid event shaping (HES): a generalized method for analyzing and designing stable hybrid event controllers. HES utilizes the saltation matrix, which gives a closed-form equation for the effect that hybrid events have on stability. We also introduce shape parameters, which are higher order terms that can be tuned completely independently of the system dynamics to promote stability. Optimization methods are used to produce values of these parameters that optimize a stability measure. Hybrid event shaping captures previously developed control methods while also producing new optimally stable trajectories without the need for continuous-domain feedback. 

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3. Robust hybrid supervisory control for rendezvous and docking of a spacecraft

   https://doi.org/10.1109/CDC.2016.7798769  

   Malladi, Bharani P.; Sanfelice, Ricardo G.; Butcher, Eric; Wang, Jingwei (December 2016, 2016 IEEE 55th Conference on Decision and Control (CDC))

   We consider the problem of rendezvous, proximity operations, and docking of an autonomous spacecraft. The problem can be conveniently divided into four phases: 1) rendezvous with angles-only measurements; 2) rendezvous with range measurements; 3) docking phase; and 4) docked phase. Due to the different constraints, available measurements, and tasks to perform on each phase, we study this problem using a hybrid systems approach, in which the system has different modes of operation for which a suitable controller is to be designed. Following this approach, we characterize the family of individual controllers and the required properties they should induce to the closed-loop system to solve the problem within each phase of operation. Furthermore, we propose a supervisor that robustly coordinates the individual controllers so as to provide a solution to the problem. Due to the stringent mission requirements, the solution requires hybrid controllers that induce convergence, invariance, or asymptotic stability properties, which can be designed using recent techniques in the literature of hybrid systems. In addition, we outline specific controller designs that appropriately solve the control problems for individual phases and validate them numerically1. 

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4. 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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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)

   Abstract 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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