Robotics Locomotion and Kinematics

Locomotion

• Locomotion is the process of causing an autonomous robot to move
• Forces must be applied to the vehicle to produce motion

Wheeled Mobile Robots (WMR)

• WMRs are a combination of various physical (hardware) and computational (software) components
• Subsystems include:
  • Sensing: measuring robot and environmental properties
  • Locomotion: how the robot moves through its environment
  • Control: generating physical actions for the robot
  • Reasoning: mapping measurements into actions
  • Communication: how robots and external operators communicate

Kinematics and Dynamics

• Kinematics: the study of motion without considering forces affecting it. It deals with the relationships between control parameters and the behavior of a system.
• Dynamics: the study of motion where forces are modeled. It deals with the relationship between force and motion.

Notation

• Posture: position (x, y) and orientation (θ)
• {XmYm}: moving frame
• {XbYb}: base frame
• q: robot posture in base frame
• R(θ): rotation matrix expressing orientation of base frame relative to moving frame

Wheels

• Rolling motion occurs along the y-axis
• Lateral slip occurs along the y-axis
• z-motion occurs along the z-axis.

Robot Wheel Parameters

• For low velocities, rolling is a wheel model
• Wheel parameters include:
  • r: wheel radius
  • v: wheel linear velocity
  • w: wheel angular velocity
  • t: steering velocity

Wheel Types

• Fixed wheel
• Centered orientable wheel
• Off-centered orientable wheel (castor wheel)
• Swedish wheel (omnidirectional property)

Examples of WMR

• Bi-wheel type robot: smooth motion, risk of slipping, sometimes uses roller-ball for balance
• Caterpillar type robot: free motion, complex structure, weakness of the frame
• Omnidirectional robot: free motion, complex structure

Mobile Robot Locomotion

• Instantaneous center of rotation (ICR) or Instantaneous center of curvature (ICC): cross point of all wheel axes

Degree of Mobility

• Degree of mobility: the freedom of robot motion
  • 0: cannot move (no ICR)
  • 1: fixed arc motion (only one ICR)
  • 2: variable arc motion (line of ICRs)
  • 3: fully free motion (ICR can be located at any position)

Degree of Steerability

• Degree of steerability: the number of centered orientable wheels that can be steered independently
  • 0: no centered orientable wheels
  • 1: one centered orientable wheel
  • 2: two mutually independent centered orientable wheels

Degree of Maneuverability

• Degree of maneuverability (δ_M): δ_M = δ_m + δ_s
  • δ_m: Degree of mobility
  • δ_s: Degree of steerability
  • Omnidirectional: δ_M = 3
  • Differential: δ_M = 2
  • Omni-Steer : δ_M = 3
  • Tricycle : δ_M = 2
  • Two-Steer: δ_M = 3

Non-holonomic Constraint

• Non-holonomic constraint: constraint on feasible velocities of a body
• Robot can move in some directions (forward, backward), but not others (sideways)

Types of Driving (Steering)

• Differential Drive: two driving wheels (plus roller-ball), sensitive to relative velocity
• Steered wheels: steering wheel + rear wheels, limited turn radius
• Synchronous Drive
• Omni-directional
• Car Drive (Ackerman Steering)

1-Differential Drive

• Posture of the robot: P = (x, y, θ)
  • (x, y): position
  • θ: orientation
• Control input: U = (v, w)
  • v: linear velocity
  • w: angular velocity
• (Notice: not for each wheel)

Motion Control

• Instantaneous center of rotation (ICR): (VR - VL)/L = VR/(R + L/2), R = L(VR + VL)/2(VR - VL). Radius of rotation
  • Straight motion: R = infinity, VR = VL
  • Rotational motion: R = 0, VR = -VL

2-Tricycle

• Three wheels, odometers on two rear wheels, steering/power via front wheel
• Control variables: steering direction (a(t)) and angular velocity (ω_s(t)) of steering wheel

Synchronous Drive

• Motion of the robot is synchronised around the point of rotation.

4-Omnidirectional

• Swedish wheel can move in any direction

5-Car Drive (Ackerman Steering)

• Used in motor vehicles
• Inside front wheel rotates sharper than outside wheel
• Reduces tire slippage

Ackerman Steering

• Lateral wheel separation(d)
• Longitudinal wheel separation(l)
• Relative steering angle of inside wheel (θ₁)
• Relative steering angle of outside wheel (θ₀)
• Distance between ICC to center of vehicle(R)
• Cot(θ₁) - Cot(θ₀) = d/l.

Summary (Mobile Robot)

• Classification of wheels
  • Fixed, centered, off-centered, Swedish
• Degree of maneuverability= degree of mobility + degree of steerability
• 5 types of driving methods
  • Differential Drive
  • Steered wheels (tricycle, bicycles, wagon)
  • Synchronous Drive
  • Omni-directional
  • Car Drive (Ackerman Steering)

This quiz explores the principles of locomotion in robotics, specifically focusing on wheeled mobile robots (WMR). It covers essential subsystems like sensing, control, and dynamics of motion. Dive into kinematics and learn how these concepts enable autonomous movement.