SPIROGRAPH TOY MODELLING USING TWO-LINK PLANAR ROBOTIC ARM IN MATLAB

Using results on the topology of moduli space of polygons (Jaggi, Ph.D. Thesis, University of Bern, 1992; Kapovich and Millson, J. Differ. Geom. 42:133---164, 1994), it can be shown that for a planar robot arm with n segments there are some values of the base-length, z (i.e., length of line joining the base of the arm with its end-effector), at which the configuration space of the constrained arm (arm with its end effector fixed) has two disconnected components, while at other values it has one connected component. We first review some of these known results relating the value of z with the connectivity of the constrained configuration space. Then the main design problem addressed in this paper is the construction of pairs of continuous inverse kinematics for arbitrary robot arms, with the property that the two inverse kinematics agree (i.e. return the same configuration) when the constrained configuration space has a single connected component, but they give distinct configurations (one in each connected component) when the configuration space of the constrained arm has two components. This design is made possible by a fundamental theoretical contribution in this paper--a classification of configuration spaces of robot arms such that the type of path that the system (robot arm) takes through certain critical values of the forward kinematics function is completely determined by the class to which the configuration space of the arm belongs. This classification result makes the aforesaid design problem tractable, making it sufficient to design a pair of inverse kinematics for each class of configuration spaces (three of them in total). The motivation for this work comes from a more extensive problem of motion planning for the end effector of a robot arm, in which the ability to continuously sample one configuration from each connected component of the constrained configuration spaces of the arm enables us to dramatically reduce the dimensionality of the space in which the planning has to be performed, without sacrificing algorithmic completeness. We start the paper with the general motivation, but address only the problem of sampling such configurations when there is no obstacle in the environment--a problem that in itself is non-trivial. We demonstrate the simplicity and the low complexity of the presented algorithm through a Javascript + HTML5 based implementation available at http://hans.math.upenn.edu/~subhrabh/nowiki/robot_arm_JS-HTML5/arm.html.

Considers the problem of modeling and controlling the impact of a two-degree-of-freedom planar robot arm against an infinitely rigid and massive surface. For this case study, the basic equations describing the motion of the robot arm are derived for noncontact and contact conditions. A control scheme is proposed on the basis of a reduced-order observer that is able to asymptotically estimate the impact-induced forces and to allow their asymptotic compensation when the robot arm is in contact with the surface. The resulting control system ensures the global asymptotic regulation of the position of the arm with an assigned impact-induced force. The case study is completed by a simulation test.

The authors propose an alternative coordinated motion control architecture for robot arms manipulating an object. The motion and the internal force of the object are resolved into the motion of each arm. Each arm is controlled, on the basis of the virtual internal model, so that they operate in coordination even if geometric errors exist in the arms and the object. The virtual internal model is a reference model driven by sensory information implemented in the controller. The proposed architecture maintains the stability of the system even if breakage of the manipulated object occurs. The control algorithm was experimentally applied to the coordinated motion control of two planar robot arms, each of which has three degrees of freedom. The results illustrate the validity of the proposed control architecture. >

This paper is proposed to solve the inverse kinematic (IK) problem of two-degree-of-freedom planar robot arm using neural networks (NN). Several NN model designs of distinct hidden neurons based on the sum of square error function of joint angle are developed and trained with generalised reduced gradient algorithm. The paper is also intended to demonstrate the modelling process of feed-forward NN topology in spreadsheet environment. The spreadsheet functions as INDEX, SUMPRODUCT, EXP, and SUMSQ; the utilities as name manager, data validation, data table, ActiveX controls, answer report, and charts; and the add-in Solver are utilised to develop the models. With the input parameters of link lengths and end-effector position and orientation, two models with the structures 5-12-1 and 5-10-1 are discovered best-capable in predicting first and second joint angles respectively. This NN-based IK technique contributes significantly to the optimal motion control of robot arm for quality processing and assembly tasks.

This paper concerns reduced-order stable controllers in a unified way for two typical examples of underactuated robots called the Acrobot and the Pendubot which are two-link planar robots moving in a vertical plane with a single actuator at joints 1 and 2, respectively. The main contributions of this paper are threefold. First, using properties of the mechanical parameters of two-link planar robots, this paper proves via a constructive procedure that stable controllers exist for a local stabilization of the upright equilibrium point (two links are in upright position) of each robot by designing a specific output with an adjustable parameter and employing the pole-zero relation of the linearized model around the equilibrium point. Second, the paper presents a design method to obtain explicitly a formula of second-order (reduced-order) stable controllers by choosing the adjustable parameter. Third, in terms of strong stabilization (stabilization with a stable controller), some new features of the Acrobot and the Pendubot are revealed and are compared with those of the cart-pendulum system. Simulation results for the two robots are presented to validate the theoretical results.

The output layer of a feedforward neural network approximates nonlinear functions as a linear combination of a fixed set of basis functions, or "features". These features are learned by the hidden-layer units, often by a supervised algorithm such as a back-propagation algorithm. This paper investigates features which are optimal for computing desired output functions from a given distribution of input data, and which must therefore be learned using a mixed supervised and unsupervised algorithm. A definition is proposed for optimal nonlinear features, and a constructive method, which has an iterative implementation, is derived for finding them. The learning algorithm always converges to a global optimum and the resulting network uses two layers to compute the hidden units. The general form of the features is derived for the case of continuous signal input, and this result is related to transmission of information through a bandlimited channel. The results of other algorithms can he compared to the optimal features, which in some cases have easily computed closed-form solutions. The application of this technique to the inverse kinematics problem for a simulated planar two-joint robot arm is demonstrated here.

A variable structure model following control (VSMFC) design method is proposed for robotics applications. The method allows the designer to model the nonlinear dynamic interactions among the different mechanical components of the robot system even when an adaptive control solution is called for to satisfy stringent performance requirements. A VSMFC design for a planar two-link robot arm is considered as an example. >

To study human motor control and learning in upper extremities, scientists widely use robotic arms to apply external forces to subject’s hand interactively. In this work, we describe the design procedure of a planar parallel manipulandum with five links and 2-DoF in a vertical plane (e.g. sagittal or frontal plane). The manipulandum works in two active and passive modes. In the passive mode, the robotic arm follows the movements of the human arm; while in the active mode, the robotic endeffector guides subject’s hand in any desired direction. In both active and passive conditions, the robot arm can be programmed to apply unexpected disturbances to the subjects hand. To control the movement of the manipulandum, we used two PID controllers with local shaft angle feedback to control the manipulandum. For the active mode, we used also a global feedback from endeffector position. As the first step for proof of concept, the whole system was simulated in MATLAB.

In this paper we design, simulate, and compare the implementation of FOPID and PID controllers in non- planar robotic manipulator arm systems with increasing degree of freedom (DOF) from two to six. A modular and iterative methodology of testing for manipulators, with any number and/or type of links, is proposed which can be tested with any metaheuristic optimization technique. In this paper we have demonstrated this model with PSO. The impact of increasing the DOF is explored in the presence of varying disturbances, and payload mass by comparing the accuracy of conventional PSO tuned FOPID controller and PSO-tuned PID controller.

Acceleration-level repetitive motion planning of redundant planar robots solved by a simplified LVI-based primal-dual neural network

The question of control and stabilization of flexible space robots is considered. Although, this approach is applicable to space robots of other configurations, for definiteness, a flexible planar two-link robot, mounted on a rigid floating platform in space, is considered. The robotic arm has two revolute joints and its links undergo elastic deformation in the plane of rotation. Based on nonlinear inversion technique, a control law is derived for controlling output variables describing the position and orientation of the platform and the joint angles of the robot. Although, the inverse controller accomplishes reference trajectory tracking, it excites the elastic modes of the arm. Using linear quadratic optimal control theory, a composite stabilizer for stabilization of the rigid and flexible modes and a decoupled flexible mode stabilizer are designed for regulating the end point of the robot to the target point and vibration suppression. Stabilization using only elastic mode velocity feedback is also considered. For large maneuvers, first the inverse controller is active, and the stabilizer is switched for regulation when the motion of the robot lies in the neighborhood of the terminal equilibrium state. Simulation results are presented to show that in the closed-loop system including the inverse controller and the stabilizer, trajectory tracking and stabilization of elastic modes are accomplished.

Robotic controllers frequently operate under constraints. Often, the constraints are imperfectly or completely unknown. In this paper, the Lagrangian dynamics of a planar robot arm are expressed as a function of a globally unknown hard constraint. Laser sensors are utilized to produce estimates of local constraints. These sensors guide the end effector over the unknown object which is denoted the learning phase. The learning phase generates noisy joint position encoders and tachometers data. A extended continuous-discrete Kalman filter based estimator processes the measurements to compute an estimated parameterization of the constraint. The output of the estimator is input to a suboptimal combiner. The gradient of the estimated parameter vector is equivalent to the tactile sensory data. During the learning phase, the combiner computes a weighted combination of estimated and sensed constraints. The controller uses the constraint estimate to guide the robot arm. Thus a feedback loop is closed around the constraints. As the statistics of the estimated constraint vector become favorable compared to the stationary statistics of the sensors, the learned constraints gradually replace the need for sensory data. A block diagram of the controller, estimator, combiner, sensors, and constraints is shown. Comparative simulations are given for various combinations of ideal and noisy data.

SUMMARYIn this study, we consider a model based robust control scheme for kinematically redundant robot manipulators that also enables the use of self motion of the manipulator to perform multiple sub-tasks (e.g., maintaining manipulability, avoidance of mechanical joint limits, and obstacle avoidance). The controller proposed ensures uniformly ultimately bounded end-effector and sub-task tracking despite the parametric uncertainty associated with the dynamic model. A Lyapunov based approach has been utilized in the controller design and extension to a non minimum set of parameters for orientation representation has been presented to illustrate the flexibility of the approach. Extensive simulation studies performed initially on a 3 link planar robot arm (for the planar case) and on a six degree of freedom (DOF) Puma type robot arm (for the 3D case with quaternion feedback) are presented to demonstrate the capabilities and the performance of the controller. The results were then experimentally tested on an actual Puma 560 robot to illustrate the feasibility of the proposed method.

This paper applied a new concept of a nonlinear model reference PID controller for a planar robot arm. The controller consists of two second order differential equations, each in terms of the angle error of a single joint from the designed trajectory. The coefficients of each differential equation are specifiable giving the ability to specify the behavior of the robot. Simulations are presented that show the ability of the robot arm with the nonlinear model reference PID controller to follow the precise designed trajectory.

Placing robots outside controlled conditions requires versatile movement representations that allow robots to learn new tasks and adapt them to environmental changes. The introduction of obstacles or the placement of additional robots in the workspace, the modification of the joint range due to faults or range-of-motion constraints are typical cases where the adaptation capabilities play a key role for safely performing the robot's task. Probabilistic movement primitives (ProMPs) have been proposed for representing adaptable movement skills, which are modelled as Gaussian distributions over trajectories. These are analytically tractable and can be learned from a small number of demonstrations. However, both the original ProMP formulation and the subsequent approaches only provide solutions to specific movement adaptation problems, e.g., obstacle avoidance, and a generic, unifying, probabilistic approach to adaptation is missing. In this paper we develop a generic probabilistic framework for adapting ProMPs. We unify previous adaptation techniques, for example, various types of obstacle avoidance, via-points, mutual avoidance, in one single framework and combine them to solve complex robotic problems. Additionally, we derive novel adaptation techniques such as temporally unbound via-points and mutual avoidance. We formulate adaptation as a constrained optimisation problem where we minimise the Kullback-Leibler divergence between the adapted distribution and the distribution of the original primitive while we constrain the probability mass associated with undesired trajectories to be low. We demonstrate our approach on several adaptation problems on simulated planar robot arms and 7-DOF Franka-Emika robots in a dual robot arm setting.