Session: 07-03-02: Design and Control of Robots, Mechanisms and Structures

Paper Number: 95079

95079 - Robust Dynamic Modeling and Trajectory Tracking Controller of a Universal Omni-Wheeled Mobile Robot 

The word “omnidirectional” means being in or involved in all directions. In robotic motion, it describes the ability of a system to move in any direction from any configuration.  Omnidirectional mobile robots are widely used in studies and services as they are effective and efficient in moving in any direction regardless of their current orientation. These significant properties are very useful in energy-efficient navigation and obstacle avoidance in dynamic environments.

The literature on modeling and control of omni-wheel robots usually relies on the kinematic model or simplified kinematic model. Then developing control laws based on these reduced-effect models. Kinematic modeling is less complex than multibody dynamic modeling. But to have an accurate simulation of the realistic motions of a mechanical system, the multibody dynamic model is required.

In classical mechanics, dynamic systems fall into two categories namely holonomic or non-holonomic. A system is holonomic if the number of controllable degrees of freedom is equal to the total degrees of freedom. To be a non-holonomic system, controllable degrees of freedom must be less than the total degrees of freedom. There appears to be no prior work that demonstrated a complete non-holonomic dynamic model of the omni-wheel systems, including roller dynamics.

In this work, we developed an efficient full dynamic model of a non-holonomic, square base configured 4-omni-wheeled mobile robot including roller dynamics, assuming no slip wheels, allowing for a PID control law to robustly follow arbitrary paths. Kane’s approach was used for the dynamic model derivation.

For the forward kinematic modeling, we used vector projection of the heading velocity onto the body frame which is easy to derive and understand.  The global velocities (x', y', theta') were given as inputs to the model and tested for various combinations like driving in a line, standing in a place and spinning etc. The simulation results demonstrated the forward kinematic model is valid for any given combination of inputs.

In the inverse kinematic modeling, we examined the behavior of the model when the inputs are the angular velocities of the four wheels. It was demonstrated that the model is valid for any given combination of wheel speeds. To derive the inverse kinematic model, the Ordinary Least Square method was used to express the kinematic differential equations.

Kane’s dynamic equations enable computer algorithms to work rapidly because the formulation is purely differential in nature. The developed dynamic model was validated using conservation of energy and momentum. For any given combination of inputs, the model demonstrated realistic behavior.  

A PID controller was developed and tested for the robot model for trajectory tracking. The model shows that it can track a given arbitrary path with very little error. First, the controller was tested for a figure-eight path covering 40 inches on a side for smooth curves. The error along the x-axis was less than 0.02% and the y-axis was less than 0.04% for a maneuvering time of 50 s. The controller required reasonable motor torques. Then, the controller was tested for a path with sharp curves with a maneuvering time of 25 s. Over the 85-inch-long path there was 0.2 inches error at the corners. Finally, the controller was tested for disturbance forces. An arbitrary force function with varying force magnitudes at different time intervals was introduced to the system while the robot tracks the figure-eight path. The results demonstrated reasonable motor torque values with a maximum tracking error of less than 0.06 inches over the given path length covering 40 inches on a side.

Presenting Author: Nalaka Amarasiri University of Louisiana at Lafayette

Presenting Author Biography: Nalaka B. Amarasiri is a PhD student of Systems Engineering at the University of Louisiana at Lafayette. He works on the robot dynamics, control and reinforcement learning area under the supervision of Dr. Alan A Barhorst and Dr. Raju Gottumukkala.

Authors:

Nalaka Amarasiri University of Louisiana at Lafayette
Alan Barhorst University of Louisiana at Lafayette
Raju Gottumukkala University of Louisiana at Lafayette