Session: 07-09-01: Vibrations of Continuous Systems

Paper Number: 112976

112976 - Model-Based Visual Control for Robotic Manipulators Using Udwadia Kalaba Formulation 

This work presents the development of a model-based visual control strategy for robotic manipulators performing target tracking. The proposed approach combines computer vision techniques for target identification with the Udwadia–Kalaba formulation for constrained robotic motion control. The Udwadia-Kalaba (UK) formulation is an explicit equation that describes the analytical dynamics of constrained motion of a mechanical system, being advantageous as it can handle both holonomic and non-holonomic constraints, and produces energy efficient control formulations.  

In this paper, the UK approach is used to design a low-level control architecture in the joint space of the robotic manipulator. First, the unconstrained dynamics of the robot is developed using Euler-Lagrange formulation. Then, we impose upon this unconstrained system, smooth constraints based on the identified target. These constraints are dependent on the states of the target (position and velocity), may be holonomic or not, and are defined as functions of time. These constraints are manipulated to be represented as second order differential equations and produce a closed form solution defined in the joint coordinate frame. This solution drives the definition of the joint torque commands required to move the manipulator and follow an identified target. Nevertheless, the base formulation of the UK strategy requires the constraints to be satisfied by the initial conditions. To address these limitations, Baumgarte’s stability analysis is used to reformulate the constraints and expand the applicability of the approach.  

The constraints of the system are defined using a visual tracking approach. A stereo camera is mounted in an eye-in-hand configuration to the robotic manipulator. The pose of a target is continuously estimated using classical image processing techniques, such as adaptive thresholding, contour extraction, and perspective transformations. The integration of the visual tracking strategy and the UK formulation using Baumgarte's approach leads to a model-based visual servoing strategy capable of stable behaviors while performing trajectory tracking, even in the case when discontinuities are present in the system. This approach is computationally efficient compared with standard model-based and visual servoing approaches. Furthermore, the proposed strategy is energy efficient since the UK method uses knowledge about the model and Gauss's principle of least constraint to achieve the required acceleration to fulfill the task while fulfilling the constraints.  

The paper will present experimental target identification using a stereo vision camera and its integration with a 4-DOF manipulator using the Robotic Operating System (ROS). The complete system will be evaluated both qualitatively and quantitatively, by requiring the manipulator to follow both predefined and random trajectories defined in the world coordinate systems.

Presenting Author: Edward Morgan Louisiana State University

Presenting Author Biography: Edward Morgan is a PhD student in Mechanical Engineering at Louisiana State University (LSU), working in the Control and Robotics Engineering (iCORE) Lab. His research is focused on developing dynamic models and controls for lightweight underwater vehicle-manipulator systems in complex environments, with the aim of enabling manipulation and grasping. Mr. Morgan is particularly interested in robot manipulation, control, perception, path planning, and mobile robots. Looking to the future, he aspires to work as an autonomous controls engineer, leveraging predictive modeling and analysis to tackle complex problems.

Authors:

Edward Morgan Louisiana State University
William Ard Louisiana State University
Corina Barbalata Louisiana State University