The hyper redundant manipulators (HRMs) have excessively many degrees of freedom. As a special but practicable subset of them, the binary hyper-redundant manipulators (BHRMs) use binary (on–off) actuators with only two stable states such as pneumatic cylinders and/or solenoids. This article describes the conceptual design of a spatial BHRM together with its forward kinematics. This BHRM consists of many modules with the same constructive characteristics. The modules increase in size from the tip to the base so that the actuator powers also increase in the same order. Each module consists of three submodules. The first and second submodules have the shapes of variable geometry trusses and they work in mutually orthogonal planes. The third submodule is a discrete twister. The manipulator is assumed to be driven by pneumatic on–off actuators. Because of the discrete nature of the on–off actuators, a small but continuously actuated six-joint manipulator is installed as the last module of the BHRM in order to compensate the discretization errors.
This article is about the position control of a binary hyper redundant manipulator, which is driven by pneumatic on-off actuators. The end platform of the binary hyper redundant manipulator bears a small fine tuning manipulator, which is a continuously actuated six-joint manipulator attached as a versatile error-compensation tool. It is employed to compensate especially the discretization errors. The position control aims to make the end-effector of the fine tuning manipulator track a specified sequence of successive poses as required by the task to be performed. This aim is achieved by solving the inverse kinematics problem of the binary hyper redundant manipulator, i.e. by determining the binary positions of the on-off actuators, so that the end platform of the binary hyper redundant manipulator enters the inverted working volume of the fine tuning manipulator for each specified target pose of the end effector. As to solve the inverse kinematics problem of the binary hyper redundant manipulator, three methods are presented. They are the plain spline fitting method, the extended spline fitting method, and the workspace filling method. The plain spline fitting method is based on forcing the actual backbone curve of the binary hyper redundant manipulator to approximate a spatial reference spline which is specified as the desired backbone curve. In the extended spline fitting method, the result found in the plain spline fitting method is improved by using a genetic algorithm. In the workspace filling method, the workspace of the binary hyper redundant manipulator is filled randomly with a sufficiently large finite number of discrete configurational samples. If it is desired to have a concentration on a particular region of the workspace, then that region is filled by using a genetic algorithm. After the filling stage, the sample closest to the desired configuration is determined by a suitable searching algorithm. The three methods are demonstrated and comparatively discussed by means of several examples.
KeywordsBinary hyper redundant manipulators, inverse kinematics of binary hyper redundant manipulators, position control of binary hyper redundant manipulators Date
The inverted pendulum systems have inherently unstable dynamics. In order to stabilize the inverted pendulum at upright position, an actuation mechanism should generate fast-reactive motions at the pivot point of the system. This paper addressed the design and control of a spatial inverted pendulum with two degrees of freedom (DOF). The first part of the study consists of designing a novel planar two-DOF (PRRRR) actuation mechanism in order to balance the spatial inverted pendulum. The system is underactuated and has inherently extreme nonlinearity and also the restrictions on the actuators. Then, in the second part, a second-order sliding-mode and a linear quadratic Gaussian (LQG) controller have been proposed to control the pendulum within the equilibrium position. Finally the simulation results evaluated in terms of the robustness, time response and stability show that the second-order sliding-mode controller is more robust and has fast response performances in re-stabilizing the spatial inverted pendulum, while LQG controller is better in terms of keeping the system in equilibrium during the long period of time. Keywords Two degrees of freedom inverted pendulum • Spatial inverted pendulum • Sliding-mode control • Linear quadratic Gaussian * Atilla Bayram
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