Robotics Locomotion and Kinematics

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Questions and Answers

What is the main focus of the study of motion?

Studying environmental impact

Understanding robot design (correct)

Building structures

Analyzing human behavior

When considering motion from above, which aspect is being analyzed?

Angular acceleration

Translational force

Linear speed (correct)

Rotational movement

What term refers to the speed at which an object travels along a curve?

Tangent speed (correct)

Radial speed

Curved velocity

Lateral speed

Which of the following describes the angle at which an object moves?

Angular velocity Signup and view all the answers

In robotic design, what does the term 'linear speed' refer to?

Speed along a straight path Signup and view all the answers

What does the term 'angular velocity' refer to in the context provided?

The rotational speed of an object around a fixed point Signup and view all the answers

What does the degree of movement depend on?

The ability to steer Signup and view all the answers

Which factor can influence the angular velocity according to the provided content?

The level of tilt applied Signup and view all the answers

If two wheels are aligned in the same direction, what can be inferred?

They will turn effectively in the same direction Signup and view all the answers

What is the implication of a fixed position of rotation in a system?

It maintains a constant angular velocity Signup and view all the answers

Which scenario indicates the inability to steer effectively?

One wheel spinning faster than the other Signup and view all the answers

What does the ability to tilt slightly around a defined point contribute to?

Increased capability for change in direction Signup and view all the answers

What characteristic is not associated with two equal wheels in the context provided?

They have different gravitational forces Signup and view all the answers

What is typically true about the center of rotation?

It is the point that remains stationary while the object rotates around it Signup and view all the answers

In the context of steering capability, which factor is least likely to influence maneuverability?

Anchor weight Signup and view all the answers

Study Notes

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)

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Description

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.