In the name of Allah

1. In the name of Allah

2. Introduction to Robotics • Leila Sharif • l_sharif@sharif.edu http://ce.sharif.edu/courses/84-85/1/ce516/ • Lecture #4: Effectors and Actuators

3. Lecture Outline • A brief history of robotics • Feedback control • Cybernetics • Artificial Intelligence (AI) • Early robotics • Robotics today • Why is robotics hard? • Degrees of Freedom (DOF) • holonomicity, redundancy • Legged locomotion • stability (static and dynamic) • polygon of support • Wheeled locomotion • Trajectory/motion planning

4. Feedback Control • Feedback: continuous monitoring of the sensors and reacting to their changes. • Feedback control = self-regulation • Two kinds of feedback: • Positive • Negative • The basis of control theory

5. - and + Feedback • Negative feedback • acts to regulate the state/output of the system • e.g., if too high, turn down, if too low, turn up • thermostats, bodies, robots... • Positive feedback • acts to amplify the state/output of the system • e.g., the more there is, the more is added • stock market, ...

6. Cybernetics • Pioneered by Norbert Wiener (1940s) • (From Greek “steersman” of steam engine) • Marriage of control theory(feedback control),information science and biology • Seeks principles common to animals and machines, especially for control and communication • Coupling an organism and its environment (situatedness)

7. Early Artificial Intelligence • “Born” in 1955 at Dartmouth • “Intelligent machine” would use internal models to search for solutions and then try them out (M. Minsky) => deliberative model! • Planning became the tradition • Explicit symbolic representations • Hierarchical system organization • Sequential execution

8. Artificial Intelligence (AI) • Early AI had a strong impact on early robotics • Focused on knowledge, internal models, and reasoning/planning • Basis of deliberative control in early robots

9. Early Robots: SHAKEY • At Stanford Research Institute (late 1960s) • Vision and contact sensors • STRIPS planner • Visual navigation in a special world • Deliberative

10. Early Robots: HILARE • LAAS in Toulouse, France (late 1970s) • Video, ultrasound, laser range-finder • Still in use! • Multi-level spatial representations • Deliberative -> Hybrid Control

11. Early Robots: CART/Rover • Hans Moravec • Stanford Cart (1977) followed by CMU rover (1983) • Sonar and vision • Deliberative control

12. Robotics Today • Assembly and manufacturing (most numbers of robots, least autonomous) • Materials handling • Gophers (hospitals, security guards) • Hazardous environments • Remote environments • Surgery (brain, hips) • Tele-presence and virtual reality • Entertainment

13. Why is Robotics hard?

14. Why is Robotics hard? • Sensors are limited and crude • Effectors are limited and crude • State (internal and external, but mostly external) is partially-observable • Environment is dynamic (changing over time) • Environment is full of potentially-useful (and useless) information

15. Key Issues • Grounding in reality:not just planning in an abstract world • Situatedness (ecological dynamics): tight connection with the environment • Embodiment: having a body • Emergent behavior: interaction with the environment • Scalability: increasing task and environment complexity

16. Definition of Effector • An effector is any device that has an effect on the environment. • A robot’s effectors are used to purposefully effect the environment. • E.g., legs, wheels, arms, fingers... • The role of the controller is to get the effectors to produce the desired effect on the environment, based on the robot’s task.

17. Definition of Actuator • An actuator is the actual mechanism that enables the effector to execute an action. • E.g, electric motors, hydraulic or pneumatic cylinders, pumps… • Actuators and effectors are not the same thing. • Incorrectly thought of the same; “whatever makes the robot act”

18. Degrees of Freedom • Most simple actuators control a single degree of freedom (DOF) • Think of DOFs as ways in which a motion can be made (e.g., up-down, left-right, in-out) • E.g., a motor shaft controls one rotational DOF; a sliding part on a plotter controls one translational DOF.

19. Counting DOF • A free body in space has 6 DOF • 3 are translational (x, y, z) • 3 are rotational (roll, pitch, and yaw) • Every robot has a specific number of DOF • If there is an actuator for every DOF, then all of the DOF are controllable • Usually not all DOF are controllable • This makes robot control harder

20. Example: DOF of a Car • A car has 3 DOF: position (x,y) and orientation (theta) • Only 2 DOF are controllable • driving: through the gas pedal and the forward-reverse gear • steering: through the steering wheel • Since there are more DOF than are controllable, there are motions that cannot be done, like moving sideways (that’s why parallel parking is hard)

21. Actuators and DOFs • We need to make a distinction between what an actuator does (e.g., pushing the gas pedal) and what the robot does as a result (moving forward) • A car can get to any 2D position but it may have to follow a very complicated trajectory • Parallel parking requires a discontinuous trajectory w.r.t. velocity, i.e., the car has to stop and go

22. Holonomicity • When the number of controllable DOF is equal to the total number of DOF on a robot, it is holonomic. • If the number of controllable DOF is smaller than total DOF, the robot is non-holonomic. • If the number of controllable DOF is larger than the total DOF, the robot is redundant.

23. Redundancy • A human arm has 7 DOF (3 in the shoulder, 1 in the elbow, 3 in the wrist), all of which can be controlled. • A free object in 3D space (e.g., the hand, the finger tip) can have at most 6 DOF! • => There are redundant ways of putting the hand at a particular position in 3D space. • This is the core of why manipulations is very hard!

24. Uses of Effectors • Two basic ways of using effectors: • to move the robot around =>locomotion • to move other object around =>manipulation • These divide robotics into two mostly separate categories: • mobile robotics • manipulator robotics

25. Locomotion • Many different kinds of effectors and actuators are used for locomotion: • legs (walking, crawling, climbing, jumping, hopping…) • wheels (rolling) • arms (swinging, crawling, climbing…) • flippers (swimming) • Most animals use legs, but most mobile robots use wheels, why?

26. Stability • Stability is a necessary property of mobile robots • Stability can be • static (standing w/o falling over) • dynamic (moving w/o falling over) • Static stability is achieved through the mechanical design of the robot • Dynamic stability is achieved through control

27. More on Stability • E.g., people are not statically stable, but are dynamically stable! It takes active control to balance. This is mostly unconscious. • Static stability becomes easier with more legs. • To remain stable, a robot’s center of gravity(COG) must fall under its polygon of support (the area of the projection of its points of contact onto the surface)

28. Polygon of Support • In two-legged robots/creatures, the polygon of support is very small, much smaller than the robot itself, so static stability is not possible (unless the feet are huge!) • As more legs are added, and the feet spread out, the polygon gets larger • Three-legged creatures can use a tripod stance to be statically stable

29. Statically Stable Walking • Three legs are enough to balance, but what about walking? • If a robot can stay continuously balanced while walking, it employs statically stable walking • Impossible with 3 legs; as soon as one is off the ground, only 2 are left, which is unstable • How many legs are needed for statically stable walking?

30. Good Numbers of Legs • Since it takes 3 legs to be statically stable, it takes at least 4 to walk statically stable • Various such robots have been built • 6 legs is the most popular number as they allow for a very stable walking gait, the tripod gait • 3 legs are kept on the ground, while the other 3 are moved forward

31. The Tripod Gait

32. The Tripod Gait • If the same three legs move at a time, this is called the alternating tripod gait • if the legs vary, it is called the ripple gait • All times, a triangle of support stays on the ground, and the COG is in it • This is very stable and thus used in most legged robots

33. Tripod Gait in Biology • Cockroaches and many other 6-legged insects use the alternating tripod gait • Note: numerous insects have 6 legs • Insects with more than 6 legs (e.g., centipedes and millipedes), use the ripple gate • Insects can also run very fast by letting go of the ground completely every once in a while, and going airborne…

34. Dynamic Stability • Statically stable walking is very energy inefficient • As an alternative, dynamic stability enables a robot to stay up while moving • This requires active control (i.e., the inverse pendulum problem) • Dynamic stability can allow for greater speed, but requires harder control

35. Wheels v. Legs • Because balance is such a hard control problem, most mobile robots have wheels, not legs, and are statically stable • Wheels are more efficient than legs, and easier to control • There are wheels in nature, but legs are by far more prevalent, though in terms of population sizes, more than 2 legs (i.e., insects abound)

36. Varieties of Wheels • Wheels are the locomotion effector of choice in most mobile robots • Wheels can be as innovative as legs • size and shape variations • tire shapes and patterns • tracks • wheels within wheels and cylinders • different directions of rotation • ...

37. Wheels and Holonomicity • Having wheels does not imply holonomicity • 2 or 4-wheeled robots are not usually holonomic • A popular and efficient design involves 2 differentially-steerable wheels and a passive caster

38. Differential Steering • Differential steering means that the two (or more) wheels can be steered separately (individually) • If one wheel can turn in one direction and the other in the opposite direction, the robot can spin in place • This is very helpful for following arbitrary trajectories • Tracks are often used (e.g., tanks)

39. Trajectories • In locomotion we can be concerned with: • getting to a particular location • following a particular trajectory (path) • Following an arbitrary given trajectory is harder, and it is impossible for some robots (depending on their DOF) • For others, it is possible, but with discontinuous velocity(stop, turn, and then go again)

40. Trajectory Planning • A large area of traditional robotics is concerned with following arbitrary trajectories • Why? Because planning can be used to compute optimal (and thus arbitrary) trajectories for a robot to follow to get to a particular goal location • Practical robots may not be so concerned with specific trajectories as with just getting to the goal location

41. More Trajectory Planning • Trajectory planning is a computationally complex process • All possible trajectories must be found (by using search) and evaluated • Since robots are not points, their geometry (i.e., turning radius) and steering mechanism (holonomicity properties) must be taken into account • This is also called motion planning