Inverse Kinematics without matrix inversion

This paper presents a new singularity robust and computationally efficient method for solving the inverse kinematics (IK) problem. In this method, the transformation from Cartesian space to joint space is performed in a feedback loop and as a result the new feedback inverse kinematics (FIK) law operates as a filter and does not require matrix manipulations (inversion, singular value decomposition or a computation of a damping factor). While the computational demand is greatly reduced, the performance is comparable to the one delivered by the damped least squares (DLS) law. The new algorithm is capable of escaping and avoiding kinematic singularities and in this respect it outperforms pseudo-inverse based formulations

Dynamic whole-body motion generation under rigid contacts and other unilateral constraints

The most widely used technique for generating wholebody motions on a humanoid robot accounting for various tasks and constraints is inverse kinematics. Based on the task-function approach, this class of methods enables the coordination of robot movements to execute several tasks in parallel and account for the sensor feedback in real time, thanks to the low computation cost. To some extent, it also enables us to deal with some of the robot constraints (e.g., joint limits or visibility) and manage the quasi-static balance of the robot. In order to fully use the whole range of possible motions, this paper proposes extending the task-function approach to handle the full dynamics of the robot multibody along with any constraint written as equality or inequality of the state and control variables. The definition of multiple objectives is made possible by ordering them inside a strict hierarchy. Several models of contact with the environment can be implemented in the framework. We propose a reduced formulation of the multiple rigid planar contact that keeps a low computation cost. The efficiency of this approach is illustrated by presenting several multicontact dynamic motions in simulation and on the real HRP-2 robot

Self-motion control of kinematically redundant robot manipulators

Thesis (Master)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2012Includes bibliographical references (leaves: 88-92)Text in English; Abstract: Turkish and Englishxvi,92 leavesRedundancy in general provides space for optimization in robotics. Redundancy can be defined as sensor/actuator redundancy or kinematic redundancy. The redundancy considered in this thesis is the kinematic redundancy where the total degrees-of-freedom of the robot is more than the total degrees-of-freedom required for the task to be executed. This provides infinite number of solutions to perform the same task, thus, various subtasks can be carried out during the main-task execution. This work utilizes the property of self-motion for kinematically redundant robot manipulators by designing the general subtask controller that controls the joint motion in the null-space of the Jacobian matrix. The general subtask controller is implemented for various subtasks in this thesis. Minimizing the total joint motion, singularity avoidance, posture optimization for static impact force objectives, which include maximizing/minimizing the static impact force magnitude, and static and moving obstacle (point to point) collision avoidance are the subtasks considered in this thesis. New control architecture is developed to accomplish both the main-task and the previously mentioned subtasks. In this architecture, objective function for each subtask is formed. Then, the gradient of the objective function is used in the subtask controller to execute subtask objective while tracking a given end-effector trajectory. The tracking of the end-effector is called main-task. The SCHUNK LWA4-Arm robot arm with seven degrees-of-freedom is developed first in SolidWorks® as a computer-aided-design (CAD) model. Then, the CAD model is converted to MATLAB® Simulink model using SimMechanics CAD translator to be used in the simulation tests of the controller. Kinematics and dynamics equations of the robot are derived to be used in the controllers. Simulation test results are presented for the kinematically redundant robot manipulator operating in 3D space carrying out the main-task and the selected subtasks for this study. The simulation test results indicate that the developed controller’s performance is successful for all the main-task and subtask objectives

Feedback control-based inverse kinematics solvers for a nuclear decommissioning robot

The article develops two novel feedback control-based Inverse Kinematics (IK) solvers. They are evaluated for a dual-manipulator mobile robotic system with application to nuclear decommissioning. The first algorithm has similarities to other feedback control based solvers, and borrows ideas from the Cyclic Coordinate Decent and the Jacobian Transpose methods. This yields a particularly straightforward algorithm with tunable Proportional-Integral-Derivative (PID) gains to determine performance. The second approach utilises a discrete-time state space modelling framework to solve the IK problem. Although the second solver is more complex to implement, preliminary simulation results for the case study example, show that it can converge quicker, and has improved immunity to the kinematic singularities that can occur in Jacobian based methods