A Recursive Algorithm for the Forward Kinematic Analysis of Robotic Systems Using Euler Angles

Forward kinematics is one of the main research fields in robotics, where the goal is to obtain the position of a robot’s end-effector from its joint parameters. This work presents a method for achieving this using a recursive algorithm that builds a 3D computational model from the configuration of a robotic system. The orientation of the robot’s links is determined from the joint angles using Euler Angles and rotation matrices. Kinematic links are modeled sequentially, the properties of each link are defined by its geometry, the geometry of its predecessor in the kinematic chain, and the configuration of the joint between them. This makes this method ideal for tackling serial kinematic chains. The proposed method is advantageous due to its theoretical increase in computational efficiency, ease of implementation, and simple interpretation of the geometric operations. This method is tested and validated by modeling a human-inspired robotic mobile manipulator (CHARMIE) in Python.

Accelerated Reduced Gradient Algorithm with Constraint Relaxation in Differential Inverse Kinematics

The Moore-Penrose pseudoinverse-based solution of the differential inverse kinematic task of redundant robots corresponds to the result of a particular optimization underconstraints in which the implementation of Lagrange’s ReducedGradient Algorithm can be evaded simply by considering the zero partial derivatives of the ”Auxiliary Function” associated with this problem. This possibility arises because of the fact that the cost term is built up of quadratic functions of the variable of optimization while the constraint term is linear function of the same variables. Any modification in the cost and/or constraint structure makes it necessary the use of the numerical algorithm. Anyway, the penalty effect of the cost terms is always overridden by the hard constraints that makes practical problems in the vicinity of kinematic singularities where the possible solution stillexists but needs huge joint coordinate time-derivatives. While in the special case the pseudoinverse simply can be deformed, inthe more general one more sophisticated constraint relaxation can be applied. In this paper a formerly proposed acceleratedtreatment of the constraint terms is further developed by the introduction of a simple constraint relaxation. Furthermore, thenumerical results of the algorithm are smoothed by a third order tracking strategy to obtain dynamically implementable solution.The improved method’s operation is exemplified by computation results for a 7 degree of freedom open kinematic chain

A geometrical formulation for the workspace of parallel manipulators

In study this paper, a geometric formulation is proposed to describe the workspace of parallel manipulators by using a recursive approach as an extension of volume generation for solids of revolution. In this approach, the workspace volume and boundary for each limb of the parallel manipulator is obtained with an algebraic formulation derived from the kinematic chain of the limb and the motion constraints on its joints. Then, the overall workspace of the mechanism can be determined as the intersection of the limb workspaces. The workspace of different kinematic chains is discussed and classified according to its external shape. An algebraic formulation for the inclusion of obstacles in the computation is also proposed. Both analytical models and numerical simulations are reported with their advantages and limitations. An example on a 3-SPR parallel mechanism illustrates the feasibility of the formulation and its efficiency.

GENERIC MODEL FOR GONIOPHOTOMETER GEOMETRIES

In this work, we present a method to describe the model of a goniophotometer for uncertainty analysis by state-of-the-art Universal Robotic Description Format (URDF). The parameters of the kinematic chain model are determined by measurements of the geometric properties of the goniophotometer. The uncertainties of the pose are determined using Monte Carlo (MC) simulations of the kinematic chain. The measured geometric uncertainties are input the MC simulations. The proposed framework enables high level description of kinematic chains for MC simulations of measurement systems. Furthermore, the uncertainty of the total system is demonstrated over the MC trials to prove a sufficient amount of MC trials. The results of this generic approach are evaluated against an existing model and the uncertainty determination of the same goniophotometer.

Structural synthesis of plane kinematic chain inversions without detecting isomorphism

A plane kinematic chain inversion refers to a plane kinematic chain with one link fixed (assigned as the ground link). In the creative design of mechanisms, it is important to select proper ground links. The structural synthesis of plane kinematic chain inversions is helpful for improving the efficiency of mechanism design. However, the existing structural synthesis methods involve isomorphism detection, which is cumbersome. This paper proposes a simple and efficient structural synthesis method for plane kinematic chain inversions without detecting isomorphism. The fifth power of the adjacency matrix is applied to recognize similar vertices, and non-isomorphic kinematic chain inversions are directly derived according to non-similar vertices. This method is used to automatically synthesize 6-link 1-degree-of-freedom (DOF), 8-link 1-DOF, 8-link 3-DOF, 9-link 2-DOF, 9-link 4-DOF, 10-link 1-DOF, 10-link 3-DOF and 10-link 5-DOF plane kinematic chain inversions. All the synthesis results are consistent with those reported in literature. Our method is also suitable for other kinds of kinematic chains.

Using a Development Platform with an STM32 Processor to Prototype an Inexpensive 4-DoF Delta Parallel Robot

This article presents a construction prototype of a delta 4-DoF (Degree of Freedom) parallel robot. The structure of kinematic chain was described and the problem of inverse kinematic was formulated and solved. The author also proposed a concept of a control system. The dynamics of the control object were specified, a decision upon the controller and its settings was made, as well as simulation control studies of manipulator drive were conducted. The article contains a description of prepared applications and procedures as well as the research results of the manipulator.

A Novel, Oriented to Graphs Model of Robot Arm Dynamics

Robotics is an interdisciplinary field and there exist several well-known approaches to represent the dynamics model of a robot arm. The robot arm is an open kinematic chain of links connected through rotational and translational joints. In the general case, it is very difficult to obtain explicit expressions for the forces and the torques in the equations where the driving torques of the actuators produce desired motion of the gripper. The robot arm control depends significantly on the accuracy of the dynamic model. In the existing literature, the complexity of the dynamic model is reduced by linearization techniques or techniques like machine learning for the identification of unmodelled dynamics. This paper proposes a novel approach for deriving the equations of motion and the actuator torques of a robot arm with an arbitrary number of joints. The proposed approach for obtaining the dynamic model in closed form employs graph theory and the orthogonality principle, a powerful concept that serves as a generalization for the law of conservation of energy. The application of this approach is demonstrated using a 3D-printed planar robot arm with three degrees of freedom. Computer experiments for this robot are executed to validate the dynamic characteristics of the mathematical model of motion obtained by the application of the proposed approach. The results from the experiments are visualized and discussed in detail.

Walking Robot for Moving on Vertical and Arbitrarily Oriented Surfaces

The article deals with the design of a walking robot with gripping devices that allow the robot to move on arbitrarily oriented surfaces in space. Such robots are relevant primarily for the inspection of various industrial structures. A model of a two-support robot with gripping devices that allow it to be attached to support surfaces with a small curvature, but arbitrarily oriented in space, is proposed. To ensure attachment to the support surfaces, the robot is designed with five degrees of freedom. An important criterion is the possibility of dexterous movement on surfaces. One of the degrees of freedom of the robot was made linear, which makes it easier to step over obstacles and allows you to implement simpler walking algorithms. When the robot is attached to the supporting surfaces by two gripping devices at once, the kinematic chain is closed. This can lead to an increase in forces and moments in the robot’s links. In this paper, it is applied to use two methods of controlling the drives of the links together – the implementation of impedance control by introducing feedback on the evaluation of the moment based on the motor currents and ensuring the pliability of the gripping devices due to its own elasticity. A mathematical simulation of the robot was carried out, which showed the possibility of reducing the forces in the robot links when attaching the robot to two support surfaces at the same time. The best results were achieved when controlling the current vector of a synchronous motor and using current signals to implement impedance control.