Presentation on theme: "Mobile Robot Locomotion"— Presentation transcript:
1 Mobile Robot Locomotion Capstone Design -- RoboticsMobile Robot LocomotionProf. Jizhong XiaoDepartment of Electrical EngineeringCity College of New York
2 Contents Introduction Classification of wheels Mobile Robot Locomotion What is a robot?Types of robotClassification of wheelsFixed wheelCentered orientable wheelOff-centered orientable wheelSwedish wheelMobile Robot LocomotionDifferential DriveTricycleSynchronous DriveOmni-directionalAckerman SteeringKinematics models of WMRSummary
3 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 surroundings2) Carry out different tasks: Locomotion or manipulation, do something physical–such as move or manipulate objects3) Re-programmable: can do different things4) Function autonomously and interact with human beings
4 Types of RobotsRobot ManipulatorsMobile Manipulators
5 Types of Robots Wheeled mobile robots Legged robots Aerial robots Underwater robotsHumanoid robots
7 Wheeled Mobile RobotsCombination of various physical (hardware) and computational (software) componentsA collection of subsystems:Locomotion: how the robot moves through its environmentSensing: how the robot measures properties of itself and its environmentControl: how the robot generate physical actionsReasoning: how the robot maps measurements into actionsCommunication: how the robots communicate with each other or with an outside operator
8 Mobile Robot Locomotion Locomotion — the process of causing an robot to move.In order to produce motion, forces must be applied to the robotMotor output, payloadDynamics – study of motion in which these forces are modeledDeals 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 systemDeals with the relationship between control parameters and the behavior of a system.
9 NotationPosture: position(x, y) and orientation
10 Non-holonomic constraint So what does that mean? Your robot can move in some directions (forwardsand backwards), but not others (side to side).The robot can instantlymove forward and back,but can not move to theright or left without thewheels slipping.Parallel parking,Series of maneuvers
11 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 radiusv = wheel linear velocityw = wheel angular velocityt = steering velocityNon-slipping and pure rollingLateral slip
13 Examples of WMR Example Smooth motion Risk of slipping Some times use roller-ball to make balanceExampleBi-wheel type robotExact straight motionRobust to slippingInexact modeling of turningCaterpillar type robotFree motionComplex structureWeakness of the frameOmnidirectional robot
14 Mobile Robot Locomotion Instantaneous center of rotation (ICR) or Instantaneous center of curvature (ICC)A cross point of all axes of the wheels
15 Mobile Robot Locomotion Differential Drivetwo driving wheels (plus roller-ball for balance)simplest drive mechanismsensitive to the relative velocity of the two wheels (small error result in different trajectories, not just speed)TricycleSteering wheel with two rear wheelscannot turn 90ºlimited radius of curvatureSynchronous DriveOmni-directionalCar Drive (Ackerman Steering)
16 Differential Drive Posture of the robot Control input v : Linear velocity of the robotw : Angular velocity of the robot(notice: not for each wheel)(x,y) : Position of the robot: Orientation of the robot
17 Differential Drive – linear velocity of right wheel – linear velocity of left wheelr – nominal radius of each wheelR – 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.,
18 Differential Drive Posture Kinematics Model (in world frame) Relation between the control input and speed of wheelsKinematic equationNonholonomic constraintH : A unit vector orthogonal to the plane of wheels
19 Basic Motion Control Instantaneous center of rotation Straight motion R : Radius of rotationStraight motionR = Infinity VR = VLRotational motionR = VR = -VL
20 Tricycle Three wheels: two rear wheels and one front wheel Steering and power are provided through the front wheelcontrol variables:steering direction α(t)angular velocity of steering wheel ws(t)The ICC must lie onthe line that passesthrough, and isperpendicular to, thefixed rear wheels
21 TricycleIf 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.
22 Tricycle Kinematics model in the robot frame ---configuration kinematics modelWith no slippage
24 Tricycle Kinematics model in the world frame ---Posture kinematics model
25 Synchronous DriveIn a synchronous drive robot, each wheel is capable of being driven and steered.Typical configurationsThree steered wheels arranged as vertices of an equilateraltriangle often surmounted by a cylindrical platformAll the wheels turn and drive in unisonThis leads to a holonomic behavior
27 Synchronous Drive All the wheels turn in unison All of the three wheels point in the same direction and turn at the same rateThis is typically achieved through the use of a complex collection of belts that physically link the wheels togetherThe vehicle controls the direction in which the wheels point and the rate at which they rollBecause all the wheels remain parallel the synchro drive always rotate about the center of the robotThe synchro drive robot has the ability to control the orientation θ of their pose directly.
29 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.
31 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.