Inverse Kinematics of a Humanoid Robot based on Conformal Geometric Algebra (original) (raw)

Inverse Kinematics Computation in Computer Graphics and Robotics Using Conformal Geometric Algebra

Advances in Applied Clifford Algebras, 2008

We focus on inverse kinematics applications in computer graphics and robotics based on Conformal Geometric Algebra. Here, geometric objects like spheres and circles that are often needed in inverse kinematics algorithms are simply represented by algebraic objects. We present algorithms for the inverse kinematics of a human arm like kinematic chain and for the grasping of robots and virtual humans. The main benefits of using geometric algebra in the virtual reality software Avalon are the easy, compact and geometrically intuitive formulation of the algorithms and the immediate computation of quaternions.

Modeling and Pose Control of Robotic Manipulators and Legs using Conformal Geometric Algebra

Computación y Sistemas, 2015

Controlling the pose of a manipulator involves finding the correct configuration of the robot's elements to move the end effector to a desired position and orientation. In order to find the geometric relationships between the elements of a robot manipulator, it is necessary to define the kinematics of the robot. We present a synthesis of the kinematical model of the pose for this type of robot using the conformal geometric algebra framework. In addition, two controllers are developed, one for the position tracking problem and another for the orientation tracking problem, both using an error feedback controller. The stability analysis is carried out for both controllers, and their application to a 6-DOF serial manipulator and the legs of a biped robot are presented. By proposing the error feedback and Lyapunov functions in terms of geometric algebra, we are opening a new venue of research in control of manipulators and robot legs that involves the use of geometric primitives, such as lines, circles, planes, spheres.

Differential and inverse kinematics of robot devices using conformal geometric algebra

Robotica, 2006

In this paper, the authors use the conformal geometric algebra in robotics. This paper computes the inverse kinematics of a robot arm and the differential kinematics of a pan–tilt unit using a language of spheres showing how we can simplify the complexity of the computations.This work introduces a new geometric Jacobian in terms of bivectors, which is by far more effective in its representation as the standard Jacobian because its derivation is done in terms of the projections of the involved points onto the line axes. Furthermore, unlike the standard formulation, our Jacobian can be used for any kind of robot joints.In this framework, we deal with various tasks of three-dimensional (3D) object manipulation, which is assisted by stereo-vision. All these computations are carried out using real images captured by a robot binocular head, and the manipulation is done by a five degree of freedom (DOF) robot arm mounted on a mobile robot. In addition to this, we show a very interesting ap...

Inverse Kinematics for Industrial Robots using Conformal Geometric Algebra

Modeling Identification and Control, 2016

This paper shows how the recently developed formulation of conformal geometric algebra can be used for analytic inverse kinematics of two six-link industrial manipulators with revolute joints. The paper demonstrates that the solution of the inverse kinematics in this framework relies on the intersection of geometric objects like lines, circles, planes and spheres, which provides the developer with valuable geometric intuition about the problem. It is believed that this will be very useful for new robot geometries and other mechanisms like cranes and topside drilling equipment. The paper extends previous results on inverse kinematics using conformal geometric algebra by providing consistent solutions for the joint angles for the different configurations depending on shoulder left or right, elbow up or down, and wrist flipped or not. Moreover, it is shown how to relate the solution to the Denavit-Hartenberg parameters of the robot. The solutions have been successfully implemented and tested extensively over the whole workspace of the manipulators.

Competitive runtime performance for inverse kinematics algorithms using conformal geometric algebra

Conformal geometric algebra is a powerful tool to find geometrically intuitive solutions. We present an approach for the combination of compact and elegant algorithms with the generation of very efficient code based on two different optimization approaches with different advantages, one is based on Maple, the other one is based on the code generator Gaigen 2. With these results, we are convinced that conformal geometric algebra will be able to become fruitful in a great variety of applications in Computer Graphics.

Inverse Kinematics of a Humanoid Robot with Non-Spherical Hip: A Hybrid Algorithm Approach

International Journal of Advanced Robotic Systems, 2013

This paper describes an approach to solve the inverse kinematics problem of humanoid robots whose construction shows a small but non negligible offset at the hip which prevents any purely analytical solution to be developed. Knowing that a purely numerical solution is not feasible due to variable efficiency problems, the proposed one first neglects the offset presence in order to obtain an approximate "solution" by means of an analytical algorithm based on screw theory, and then uses it as the initial condition of a numerical refining procedure based on the Levenberg-Marquardt algorithm. In this way, few iterations are needed for any specified attitude, making it possible to implement the algorithm for real-time applications. As a way to show the algorithm's implementation, one case of study is considered throughout the paper, represented by the SILO2 humanoid robot.

Closed-Form Inverse Kinematic Joint Solution for Humanoid Robots

— This paper focuses on developing a consistent methodology for deriving a closed-form inverse kinematic joint solution of a general humanoid robot. Most humanoid-robot researchers resort to iterative methods for inverse kinematics using the Jacobian matrix to avoid the difficulty of finding a closed-form joint solution. Since a closed-form joint solution, if available, has many advantages over iterative methods, we have developed a novel reverse decoupling mechanism method by viewing the kinematic chain of a limb of a humanoid robot in reverse order and then decoupling it into the positioning and orientation mechanisms, and finally utilizing the inverse transform technique in deriving a consistent joint solution for the humanoid robot. The proposed method presents a simple and efficient procedure for finding the joint solution for most of the existing humanoid robots. Extensive computer simulations of the proposed approach on a Hubo KHR-4 humanoid robot show that it can be applied easily to most humanoid robots with slight modifications.

Inverse Kinematics Solution for Biped Robot

A biped is a multi-jointed mechanism that performs a human's motions. It seems more difficult to analyze the behavioral character of walking robot due to the complexity of mathematical description. This paper focuses on developing a methodology for deriving an inverse kinematic joint solution of a biped robot. This work aimed to build the lower side, the locomotion part of a biped robot. It couples a design considerations and simplicity of design to provide inverse kinematics analysis of 11 degree-of-freedom (DOF) biped robot. The model used consists of 5-links which are connected through revolute joints. The identical legs have hip joint, knee joints and ankle joint. This paper addresses symbolic formulation for reducing problem in solving univariate polynomial. An effective approach is developed for the solution of inverse kinematics task in analytical form for given end-effector position. This method presents a simple and efficient procedure for finding the joint solution of bipeds.