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Capstone Design -- Robotics. Mobile Robot Locomotion . Prof. Jizhong Xiao Department of Electrical Engineering City College of New York Contents. Introduction What is a robot? Types of robot Classification of wheels Fixed wheel Centered orientable wheel

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Mobile robot locomotion

Capstone Design -- Robotics

Mobile Robot Locomotion

Prof. Jizhong Xiao

Department of Electrical Engineering

City College of New York

Mobile robot locomotion


  • Introduction

    • What is a robot?

    • Types of robot

  • Classification of wheels

    • Fixed wheel

    • Centered orientable wheel

    • Off-centered orientable wheel

    • Swedish wheel

  • Mobile Robot Locomotion

    • Differential Drive

    • Tricycle

    • Synchronous Drive

    • Omni-directional

    • Ackerman Steering

  • Kinematics models of WMR

  • Summary

What is a robot
What is a robot?

  • There’s no precise definition, but by general agreement, Robots — machines with sensing, intelligence and mobility.

  • To be qualified as a robot, a machine has to be able to:

    1) Sensing and perception: get information from its surroundings

    2) Carry out different tasks: Locomotion or manipulation, do something physical–such as move or manipulate objects

    3) Re-programmable: can do different things

    4) Function autonomously and interact with human beings

Types of robots
Types of Robots

  • Robot Manipulators

  • Mobile Manipulators

Types of robots1
Types of Robots

  • Wheeled mobile robots

  • Legged robots

  • Aerial robots

  • Underwater robots

  • Humanoid robots

Wheeled mobile robots
Wheeled Mobile Robots

  • Combination of various physical (hardware) and computational (software) components

  • A collection of subsystems:

    • Locomotion: how the robot moves through its environment

    • Sensing: how the robot measures properties of itself and its environment

    • Control: how the robot generate physical actions

    • Reasoning: how the robot maps measurements into actions

    • Communication: how the robots communicate with each other or with an outside operator

Mobile robot locomotion1
Mobile Robot Locomotion

  • Locomotion — the process of causing an robot to move.

    • In order to produce motion, forces must be applied to the robot

    • Motor output, payload

  • Dynamics – study of motion in which these forces are modeled

    • Deals with the relationship between force and motions.

  • Kinematics – study of the mathematics of motion without considering the forces that affect the motion.

    • Deals with the geometric relationships that govern the system

    • Deals with the relationship between control parameters and the behavior of a system.


Posture: position(x, y) and orientation 

Non holonomic constraint
Non-holonomic constraint

So what does that mean? Your robot can move in some directions (forwards

and backwards), but not others (side to side).

The robot can instantly

move forward and back,

but can not move to the

right or left without the

wheels slipping.

Parallel parking,

Series of maneuvers

Idealized rolling wheel
Idealized Rolling Wheel

  • Assumptions:

    • No slip occurs in the orthogonal direction of rolling (non-slipping).

    • No translation slip occurs between the wheel and the floor (pure rolling).

    • At most one steering link per wheel with the steering axis perpendicular to the floor.

  • Wheel parameters:

    • r = wheel radius

    • v = wheel linear velocity

    • w = wheel angular velocity

    • t = steering velocity

Non-slipping and pure rolling

Lateral slip

Wheel types
Wheel Types

Fixed wheel

Centered orientable wheel

Off-centered orientable wheel

(Castor wheel)

Swedish wheel:omnidirectional property

Examples of wmr
Examples of WMR

  • Smooth motion

  • Risk of slipping

  • Some times use roller-ball to make balance


Bi-wheel type robot

  • Exact straight motion

  • Robust to slipping

  • Inexact modeling of turning

Caterpillar type robot

  • Free motion

  • Complex structure

  • Weakness of the frame

Omnidirectional robot

Mobile robot locomotion2
Mobile Robot Locomotion

  • Instantaneous center of rotation (ICR) or Instantaneous center of curvature (ICC)

    • A cross point of all axes of the wheels

Mobile robot locomotion3
Mobile Robot Locomotion

  • Differential Drive

    • two driving wheels (plus roller-ball for balance)

    • simplest drive mechanism

    • sensitive to the relative velocity of the two wheels (small error result in different trajectories, not just speed)

  • Tricycle

    • Steering wheel with two rear wheels

    • cannot turn 90º

    • limited radius of curvature

  • Synchronous Drive

  • Omni-directional

  • Car Drive (Ackerman Steering)

Differential drive
Differential Drive

  • Posture of the robot

  • Control input

v : Linear velocity of the robot

w : Angular velocity of the robot

(notice: not for each wheel)

(x,y) : Position of the robot

: Orientation of the robot

Differential drive1
Differential Drive

– linear velocity of right wheel

– linear velocity of left wheel

r – nominal radius of each wheel

R – instantaneous curvature radius of the robot trajectory (distance from ICC to the midpoint between the two wheels).

Property: At each time instant, the left and right wheels must follow a trajectory that moves around the ICC at the same angular rate , i.e.,

Differential drive2
Differential Drive

Posture Kinematics Model (in world frame)

  • Relation between the control input and speed of wheels

  • Kinematic equation

  • Nonholonomic constraint

H : A unit vector orthogonal to the plane of wheels

Differential drive3
Differential Drive

Configuration Kinematics Model (in robot frame)

Basic motion control
Basic Motion Control

  • Instantaneous center of rotation

R : Radius of rotation

  • Straight motion

    R = Infinity VR = VL

  • Rotational motion

    R = 0 VR = -VL


  • Three wheels: two rear wheels and one front wheel

  • Steering and power are provided through the front wheel

  • control variables:

    • steering direction α(t)

    • angular velocity of steering wheel ws(t)

The ICC must lie on

the line that passes

through, and is

perpendicular to, the

fixed rear wheels


  • If the steering wheel is set to an angle α(t) from the straight-line direction, the tricycle will rotate with angular velocity w(t) about a point lying a distance R along the line perpendicular to and passing through the rear wheels.


Kinematics model in the robot frame

---configuration kinematics model

With no slippage


Kinematics model in the world frame

---Posture kinematics model

Synchronous drive
Synchronous Drive

  • In a synchronous drive robot, each wheel is capable of being driven and steered.

  • Typical configurations

    • Three steered wheels arranged as vertices of an equilateral

    • triangle often surmounted by a cylindrical platform

    • All the wheels turn and drive in unison

  • This leads to a holonomic behavior

Synchronous drive2
Synchronous Drive

  • All the wheels turn in unison

  • All of the three wheels point in the same direction and turn at the same rate

    • This is typically achieved through the use of a complex collection of belts that physically link the wheels together

  • The vehicle controls the direction in which the wheels point and the rate at which they roll

  • Because all the wheels remain parallel the synchro drive always rotate about the center of the robot

  • The synchro drive robot has the ability to control the orientation θ of their pose directly.

Synchronous drive3
Synchronous Drive

  • Control variables (independent)

    • v(t), w(t)

Synchronous drive4
Synchronous Drive

  • Particular cases:

    • v(t)=0, w(t)=w during a time interval ∆t, The robot rotates in place by an amount w ∆t .

    • v(t)=v, w(t)=0 during a time interval ∆t , the robot moves in the direction its pointing a distance v ∆t.

Omni directional

Swedish Wheel

Car drive ackerman steering
Car Drive (Ackerman Steering)

  • Used in motor vehicles, the inside front wheel is rotated slightly sharper than the outside wheel (reduces tire slippage).

  • Ackerman steering provides a fairly accurate dead-reckoning solution while supporting traction and ground clearance.

  • Generally the method of choice for outdoor autonomous vehicles.

Ackerman steering1
Ackerman Steering

  • The Ackerman Steering equation:

    • cot i- cot o=d/l

  • where

    • d = lateral wheel separation

    • l = longitudinal wheel separation

    • i= relative angle of inside wheel

    • o= relative angle of outside wheel


  • What is a robot?

  • Types of robots

  • Classification of wheels

  • Mobile robot locomotion

    • 5 types

  • Kinematics model of WMR


  • Read chapters 2 and 4 of the text book

  • Build robot body using LEGO blocks

  • Build robot gripper