ECE 450 Introduction to Robotics

ECE 450 Introduction to Robotics Section: 50883 Instructor: Linda A. Gee 10/14/99 Lecture 12

Dead Reckoning • Term Dead Reckoning was derived from a former sailing term: Deduced Reckoning • Mathematical procedure to determine present location of an object by advancing previous position through known course and velocity

Dead Reckoning cont’d • To calculate heading, the system counts the wheel rotations to obtain longitudinal displacement and uses frictional driven steering • Implementations • Odometry: instrumentation with optical encoders coupled with motor armatures or wheel axes • Magnetic or Inductive proximity sensors with velocity feedback information

Heading • Function is derived from an onboard steering angle sensor • Supplied by a magnetic compass or gyro • Calculated from differential odometry • incremental displacement along a path that is broken into x, y components in terms of elapsed time and distance traveled • xn+1 = xn + D sin • yn+1 = yn + Dcos

Brush encoders Potentiometers Synchros Resolves Optical encoders Magnetic encoders Inductive encoders Capacitive encoders Odometry Sensors Rotational displacement and velocity sensors

Potentiometers • Low cost rotational displacement sensors • Easy sensors to integrate • Apply voltage divider • Disadvantage: poor reliability due to dust and dirt build up

Synchros • Rotating electromagnetic device that transmits angular information electrically • Forms a variable-coupling transformer • Types of synchros • transmitters, receivers • differentials • control transformers, linear transformers • resolvers, differential resolvers • transolvers

Synchros cont’d • Most widely used synchro: • 3-phase transmitter/receiver pair • Synchro receiver is electrically identical to the transmitter

Resolver • Special configuration of the synchro • Gives voltages proportional to the sin and cos of the rotor angle • Offers a rugged, reliable means for quantifying absolute angular position • Advantages: accurate, low cost, small physical requirements

Optical Encoders • Developed in the mid-1940s by the Baldwin Piano Company for electric organs to mimic the sound of other musical instruments • Advantages: digital output, low cost, reliable, immune to noise • Types of encoders • incremental • absolute

Incremental Encoders • Easier to integrate than absolute encoders • Example: • Single channel tachometer encoder uses square wave pulses for each shaft revolution • Trade-off: resolution vs. rate • Phase quadrature incremental encoders are immune to low speed instabilities due to the use of a second channel

Absolute Encoders • Used for slower rotational applications • Infrequent rotations • steering angle • Disadvantages • Not tolerant of power interruption • Operational limitations with temperature

Doppler and Inertial Navigation • These techniques are employed to reduce the effects of slippage during navigation • Doppler Navigation • used in maritime and aeronautical applications to yield velocity measurements • principle of operation: based on Doppler shift in frequency observed when radiated energy reflects from a surface that is moving with respect to the emitter

Doppler Navigation cont’d • Other applications of Doppler Navigation include • Maritime systems: acoustical energy is reflected from the ocean floor • Airborne systems: sense microwave RF energy bouncing off the surface of the earth

Inertial Navigation • Developed originally for the deployment of aircraft • Technique later applied to missles and nuclear submarines • Inertial Navigation • Principle of operation: senses minute accelerations in each directional axes; integrating over time to derive velocity and position • uses gyroscopes and accelerometers

Design Issues for Drive and Steering Configurations • Maneuverability • translate or change direction of motion with respect to the environment • Controllability • hardware, software to control mobility • Traction • minimize slippage under variable conditions • Climbing • traverse discontinuities in floor or ground surface

Design Issues cont’d • Stability • sufficient stability for the payload to address • safety, accleration, tilt, and roll • Efficiency • power consumption and conservation issues • Maintenance • ease of maintaining components functionally

Design Issues concluded • Environmental impact • drive and steering mechanisms do not impace the floor or ground • Navigational considerations • dead reckoning considerations with respect to the surroundings

Navigational Approaches • Differential Steering • consists of two individually controlled wheels • spin in place • maneuver through congested areas • Ackerman Steering • automotive industry uses this approach • inside front wheel rotates at a sharper angle than the outside wheel in a turn • reduces tire slippage • provides accurate dead reckoning • good choice for outdoor autonomous vehicles

Navigational Approaches cont’d • Synchro Drive • uses three or more wheels that are mechanically coupled • wheels rotate in the same direction at the same speed • offers reduced slippage since all wheels generate equal and parallel force vectors at all times • three-point configuration works well for stability and traction • use a steering angle encoder to address heading

Navigational Approaches cont’d • Tricycle Drive • uses a single driven front wheel • two passive rear wheels • center of gravity moves away from the front wheel when approaching an incline which leads to loss of traction

Navigational Approaches concluded • Omni-Directional Drive • Derive the position and velocity from the motor in terms of • tangential velocity of each wheel • rotational speed of each motor • rotational rate of the base • wheel radius

Internal Position Error Correction • Uses absolute encoders to comprise a compliant linkage rotary encoders • Compliant linkage addresses • momentary controller errors without transferring any force • eliminates wheel slippage • Provides heading reference information in terms of world coordinates

ECE 450 Introduction to Robotics