Technical Cognitive Systems

Transcription

1

2 Part XII Actuators

3 3 Outline Robot Bases Hardware Components Robot Arms

4 4 Outline Robot Bases Hardware Components Robot Arms

5 5 (Wheeled) Locomotion Goal: Bring the robot to a desired pose (x, y, θ): (position in x-axis, position in y-axis, angle with x-axis) 3 Degrees of Freedom (DOF).

6 6 (Wheeled) Locomotion Goal: Bring the robot to a desired pose (x, y, θ): (position in x-axis, position in y-axis, angle with x-axis) 3 Degrees of Freedom (DOF) Many robots have less controllable degrees of freedom.

7 7 Wheel Types

8 8 Robot Bases Ackermann steering differential-drive turnable wheel omniwheel mecanum-wheel

9 9 Ackerman-Steering car-like steering robust but hard to control (parking!) Issue: Outer wheels moves on a circle of different radius than inner wheel. steering angle should be different!

10 10 Differential-Drive Turns on spot Good choice for round robots Parking is easier

11 Turnable wheels Omnidirectional (can drive forwards, sideways and turn) On change of direction, requires reconfiguration of its wheels. Controllers should not oscillate PR2: Double wheel construction to reduce friction while turning the wheel Robot Bases Hardware Components Robot Arms 11

12 12 Omniwheels Omnidirectional (can drive forwards, sideways and turn) Wheels have free rollers at 90 o Three wheels are enough Hard to make them run smooth

13 Mecanum-Wheels Omnidirectional (can drive forwards, sideways and turn) Wheels have free rollers at 45o No reconfiguration is involved Depending on wheels, requires flat ground Linearity A (linear) combination of cartesian movements can be achieved with the linear combination of the respective wheel velocities. Robot Bases Hardware Components Robot Arms 13

14 14 Control of robot bases Cartesian pose in the plane: x x = y θ Wheel positions: q 1 q =... q n The forward kinematics, relating q to x is nonlinear and hard to work with.

15 15 Control of robot bases It s easier to use its derivatives: Cartesian Velocity ẋ ẋ = ẏ θ Wheel Velocities: q = q 1... q n These velocities are related by a matrix: The Jacobian matrix J q = Jẋ

16 16 Example: Omniwheel Kinematics orange: free roller turning green: wheel turning blue: resulting movement Forward: ( q 1, q 2, q 3 ) = (0, cos(30 o ), cos(30 o ))...

17 17 Outline Robot Bases Hardware Components Motors Encoders Gearboxes Robot Arms

18 18 Stepper Motor very standardized strong at low speeds used in printers moves repeatably feedforward by nature looses steps when friction/inertia/... is too high or is moving at its resonance frequency

19 19 Brushed DC Motor cheap used in toys turns without motor controller commutation with brushes (may wear out)

20 20 Brushless DC Motor cheap as well used e.g. in CDROM drives electronic commutation necessary (with sensors or sensorless) coils can be inside or outside (better cooling when outside)

21 21 Pulse Width Modulation (PWM) transistors are efficient when either on or off (not so efficient in between) switch the power on and off at a high freqency (and let the motor do the low-pass filtering)

22 22 Optical Encoders Robots typically use wheels for movement. If we measure how much the wheels travel, we can approximate our position. Typical Solution: Optical Encoders on the shaft of the wheels (or motors).

23 23 Absolute Optical Encoders Characteristics: They give the absolute position at all times. (Really only useful if the encoder does not turn more than once). Expensive Requires log 2 n tracks and sensors for a resolution of n ticks/rev.

24 24 Absolute Optical Encoders (2) Two main types: Binary code (b) Gray code (a). Advantage: Only one bit changes at a time.

25 25 One-track absolute encoder absolute encoder with only one track still needs log 2 n sensors mounted at precise positions!

26 26 Incremental Optical Encoders They are simpler: Only one track. They only give information about direction and ammount of rotation in steps (known as ticks ) That s OK: We can keep a counter in memory for the position. The direction is known using two IR receivers, placed as to receive the light from the emitter with a 90 degree phase difference. It also allows to quadruple the resolution of the disc. (400 ticks from a disc with 100 stripes).

27 Incremental Optical Encoders (2) Robot Bases Hardware Components Robot Arms 27

28 28 Incremental Optical Encoders (2)

29 29 Planetary (=Epicyclic) Gearbox good gear ratios good torque transmission very little play

30 Harmonic-Drive Gearbox very high gear ratio acceptable torque transmission highly nonlinear friction (practically) no play Roboteach Bases rotation of the inner ellipse Hardware moves Components the outer gear one tooth forward. Robot Arms 30

31 31 Cycloidal Gearbox very high gear ratio high torque transmission used in industrial robots prone to vibrations (practically) no play

32 32 Outline Robot Bases Hardware Components Robot Arms

33 33 Robot Arms How many degrees of freedom do we need?

34 34 Robot Arms How many degrees of freedom do we need? (It depends on the task!)

35 35 Robot Arms How many degrees of freedom do we need? (It depends on the task!) pointing a camera:

36 36 Robot Arms How many degrees of freedom do we need? (It depends on the task!) pointing a camera: 2 DOF

37 37 Robot Arms How many degrees of freedom do we need? (It depends on the task!) pointing a camera: 2 DOF placing an object (only position is important):

38 38 Robot Arms How many degrees of freedom do we need? (It depends on the task!) pointing a camera: 2 DOF placing an object (only position is important): 3 DOF

39 39 Robot Arms How many degrees of freedom do we need? (It depends on the task!) pointing a camera: 2 DOF placing an object (only position is important): 3 DOF placing an object (position and orientation):

40 40 Robot Arms How many degrees of freedom do we need? (It depends on the task!) pointing a camera: 2 DOF placing an object (only position is important): 3 DOF placing an object (position and orientation): 6 DOF

41 41 Robot Arms How many degrees of freedom do we need? (It depends on the task!) pointing a camera: 2 DOF placing an object (only position is important): 3 DOF placing an object (position and orientation): 6 DOF imitating a human arm:

42 42 Robot Arms How many degrees of freedom do we need? (It depends on the task!) pointing a camera: 2 DOF placing an object (only position is important): 3 DOF placing an object (position and orientation): 6 DOF imitating a human arm: 7 DOF (from shoulder ball joint)

43 43 Industrial Robots vs. Mobile Service Robots big & heavy high speed & accuracy powerful dangerous small & lightweight lower speed & accuracy reqirements better mass / payload ratio must be safer

44 44 An Example Lighweight Robot The Kuka LWR light (15kg) still strong (14kg payload on streched arm) brushless DC motors harmonic drive gearboxes impedance control to make it soft and safe What if impedance control fails? Still safer than industrial robots (it has less inertia).

45 45 Control Challenge Industrial robots have stiff joints ( PD control is enough) The LWR has elastic joints. modeled as two coupled spring-damper-mass systems

46 46 Control Challenge II contains 4 energy buffers 4 values are required to describe the dynamic state of a joint. Effectively, requires more measurements per joint to control it well, e.g. a torque sensor after reduction. The state chosen for the LWR is (q, q, τ, τ)

47 47 State Feedback Controller NOTE: This controller compensates the dynamics of the actual joint The State Feedback Control Law used in this robot is of the form: τ M = K P q e K D q e K T τ e K S τ e + Feedforward Where (q e, q e, τ e, τ e ) are the errors of the actual positions/torques w.r.t. the desired positions/torques. Feedforward term includes: gravity compensation, friction compensation, inertia, coriolis, etc. The torque sensor also allows to estimate gearbox friction and to precisely measure external torques.

48 48 Impedance Control Interface NOTE: The user interface, assuming an idealized joint Control Strategies: Position Control (May lead to strong forces) Force Control (May lead to far position offsets) Impedance Control: Force and Position are coupled: K: Stiffness D: Damping m: Mass (not controlled) τ = K(q desired q actual ) D q m q

49 49 PR2 Arms Second Example: PR2 Arms 7 DOF arms mechanical gravity compensation 2 infinite joints weak BLDC motors (< 10W) belt transmissions payload about 2 kg flexible joints but missing extra sensors lower performance, lower gains, damping... but still good enough! Intrinsically safe, no matter what the controllers do!

50 50 Gravity Compensation Just the law of the lever τ = L F

51 51 Gravity Compensation Just the law of the lever When the arm is inclined, we need to project the force... τ = cos(α) L F

52 Gravity Compensation Just the law of the lever When the arm is inclined, we need to project the force or the lever! τ = cos(α) L F Easy to calculate (just discard the vertical component of the center of mass!) 52

53 References Wheeled Locomotion Handbook of Robotics Some more extensive lecture notes: fer/cmsc828/classes/cse pdf Components Wikipedia Robot arms (Advanced): Albu-Schäffer, Alin : Regelung von Robotern mit elastischen Gelenken am Beispiel der DLR-Leichtbaumarme 53

54 54 Credits The contents of this lecture was composed of material from various sources, including: Wikipedia Course EML2322L from University of Florida: Projects/ Background Information/Background Information.htm