Holonomic Robot Kinematics

Introduction

Holonomic robots are capable of moving in any direction without any constraints on their movement. This lesson focuses on the kinematics of such robots, which is essential for understanding their motion and control.

Key Concepts

Kinematic Model

The kinematic model of a holonomic robot can be described using a set of equations that relate the robot's input velocities to its output motions.

Velocity Equations

For a differential drive robot:

The linear and angular velocities can be represented as:

V_x = R * (w_r + w_l) / 2
V_y = 0
ω = R * (w_r - w_l) / L
            

Where:

• V_x: Linear velocity in the x-direction
• V_y: Linear velocity in the y-direction
• ω: Angular velocity
• w_r: Angular velocity of the right wheel
• w_l: Angular velocity of the left wheel
• R: Radius of the wheel
• L: Distance between the wheels

Control Strategies

To control a holonomic robot, you can implement various strategies, such as:

• Proportional-Derivative Control (PD)
• Linear Quadratic Regulator (LQR)
• Model Predictive Control (MPC)

Code Example

The following code snippet demonstrates a simple implementation of holonomic control using Python:

import numpy as np

class HolonomicRobot:
    def __init__(self, radius, distance):
        self.radius = radius  # Wheel radius
        self.distance = distance  # Wheel distance

    def compute_velocities(self, w_r, w_l):
        V_x = self.radius * (w_r + w_l) / 2
        V_y = 0  # Assuming only x movement for simplicity
        omega = self.radius * (w_r - w_l) / self.distance
        return V_x, V_y, omega

robot = HolonomicRobot(radius=0.1, distance=0.5)
velocities = robot.compute_velocities(w_r=1.0, w_l=0.5)
print("V_x:", velocities[0], "V_y:", velocities[1], "ω:", velocities[2])
                

FAQ