Underactuated robotics: A review <s> Open-loop controls <s> Methods for steering systems with nonholonomic c.onstraints between arbitrary configurations are investigated. Suboptimal trajectories are derived for systems that are not in canonical form. Systems in which it takes more than one level of bracketing to achieve controllability are considered. The trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. A class of systems that can be steered using sinusoids (claimed systems) is defined. Conditions under which a class of two-input systems can be converted into this form are given. > <s> BIB001 </s> Underactuated robotics: A review <s> Open-loop controls <s> INTRODUCTION: Brief History. Multifingered Hands and Dextrous Manipulation. Outline of the Book. Bibliography. RIGID BODY MOTION: Rigid Body Transformations. Rotational Motion in R3. Rigid Motion in R3. Velocity of a Rigid Body. Wrenches and Reciprocal Screws. MANIPULATOR KINEMATICS: Introduction. Forward Kinematics. Inverse Kinematics. The Manipulator Jacobian. Redundant and Parallel Manipulators. ROBOT DYNAMICS AND CONTROL: Introduction. Lagrange's Equations. Dynamics of Open-Chain Manipulators. Lyapunov Stability Theory. Position Control and Trajectory Tracking. Control of Constrained Manipulators. MULTIFINGERED HAND KINEMATICS: Introduction to Grasping. Grasp Statics. Force-Closure. Grasp Planning. Grasp Constraints. Rolling Contact Kinematics. HAND DYNAMICS AND CONTROL: Lagrange's Equations with Constraints. Robot Hand Dynamics. Redundant and Nonmanipulable Robot Systems. Kinematics and Statics of Tendon Actuation. Control of Robot Hands. NONHOLONOMIC BEHAVIOR IN ROBOTIC SYSTEMS: Introduction. Controllability and Frobenius' Theorem. Examples of Nonholonomic Systems. Structure of Nonholonomic Systems. NONHOLONOMIC MOTION PLANNING: Introduction. Steering Model Control Systems Using Sinusoids. General Methods for Steering. Dynamic Finger Repositioning. FUTURE PROSPECTS: Robots in Hazardous Environments. Medical Applications for Multifingered Hands. Robots on a Small Scale: Microrobotics. APPENDICES: Lie Groups and Robot Kinematics. A Mathematica Package for Screw Calculus. Bibliography. Index Each chapter also includes a Summary, Bibliography, and Exercises <s> BIB002 </s> Underactuated robotics: A review <s> Open-loop controls <s> This paper presents an adaptive gain-scheduled backstepping control ( AGSBC ) scheme for the balance control of an underactuated mechanical power-line inspection ( PLI ) robotic system with two degrees of freedom and a single control input. First, a nonlinear dynamic model of the balance adjustment process of the PLI robot is constructed, and then the model is linearized at a nominal equilibrium point to overcome the computational infeasibility of the conventional backstepping technique. Second, to solve generalized stabilization control issue for underactuated systems with multiple equilibrium points, an equilibrium manifold linearized model is developed using a scheduling variable, and then a gain-scheduled backstepping control ( GSBC ) scheme for expanding the operational area of the controlled system is constructed. Finally, an adaptive mechanism is proposed to counteract the impact of external disturbances. The robust stability of the closed-loop system is ensured by Lyapunov theorem. Simulation results demonstrate the effectiveness and high performance of the proposed scheme compared with other control schemes. <s> BIB003
Open-loop control is interesting for several reasons. It is an essential technique for automation. Open-loop control could offer cheaper and faster control for some operations. Vibratory feeders and sorters, and the remote center compliance device for peg in the hole insertions, are good examples. Open-loop stable strategies may be used as a core around which closed-loop control is organized. This may make open-loop control more robust by reducing the demands on the feedback controller. Finally, understanding open-loop stable strategies may aid in understanding the key features to be learned by a UR. Open-loop control of chain systems. The simplest chain system is a so-called single-chain system with two inputs, n state outputs. A chain system with more than two inputs is called a multi-chain system. Open-loop control methods widely used in chain systems include time polynomial input control and trigonometric function input control. The feedback control method adopted has the characteristics of optimal control. For the chain system, the time polynomial input control is a relatively simple control method, which could be obtained by solving the solution method of the undetermined coefficient method. It is easy to obtain a smooth system motion. The trigonometric function input control is a step based on the optimal control principle. The trigonometric function input control is a step-by-step control method. When the output state of the chain system is large, the output state of the pre-control to the target value would change around the target value in the subsequent control, making the stability of the system poor. The open-loop control method is implemented. The smoothness of the system motion is poor. Murray et al. BIB002 BIB001  studied the trigonometric function control algorithm of a chain system. Open-loop control with oscillating input. An open-loop control for underactuated mechanical systems using an oscillatory input with amplitude and frequency modulations BIB003 is studied. Once all of the actuating joints have moved to their desired positions, an oscillating input is applied to the actuating joint to move the remaining underactuated joints. The steering force of the underactuated joints is achieved by utilizing the dynamic coupling between actuated and underactuated joints. This dynamic coupling occurs due to the oscillatory motions of the actuated joint. Once the frequency of the oscillatory input is determined, the amplitude is decided by analyzing a time-invariant system derived from the underactuated joint dynamics by the method of averaging. By generating equations and coordinate transformations derived from the generated equations, a systematic approach is proposed for converting underactuated joint dynamics into a standard average form. In the event of an actuator failure in the external space, the failed joint could be manipulated by adopting the proposed method.