Introduction to Robotics Kinematics and Motion Planning

I2R Information Sheet Instructor: Hector Rotstein Phone: 052 37 198 47. Evenings only! Office hours: Tuesday afternoons (by appointment only) E-mail: hector@ee.technion.ac.il

I2R Information Sheet Assistant: Amir Geva Phone: 058-4296185 Office hours: Tuesday 14:30-15:30 E-mail: amirgeva@cs.technion.ac.il

Bibliography John Craig, “Introduction to robotics,” Addison Wesley. Jean-Claude Latombe, “ Robot Motion Planning,” Kluger International Series in Engineering and Computer Science. Handouts

Course Objectives At the end of this course, you should be able to: Describe and analyze rigid motion. Write down manipulator kinematics and operate with the resulting equations Solve simple inverse kinematics problems. Solve basic motion planning problems.

Syllabus A brief history of robotics. Coordinates and Coordinates Inversion. Trajectory planning. Sensors. Actuators and control. Why robotics? Basic Kinematics. Introduction. Reference frames. Translation. Rotation. Rigid body motion. Velocity and acceleration for General Rigid Motion. Relative motion. Homogeneous coordinates. Robot Kinematics. Forward kinematics. Link description and connection. Manipulator kinematics. The workspace.

Syllabus (cont.) Inverse Kinematics. Introduction. Solvability. Inverse Kinematics. Examples. Repeatability and accuracy. Velocity. The Jacobian. Trajectory generation. Introduction. General considerations. Path generation. Motion Planning. Introduction. Algorithms for motion planning.

Policies and Grades There will be six homework assignments, a mid-term exam and a project. The exam will be open book. The homework will count 6% each towards the final grade, the test 36% and the project 28%. The worst homework will be given 20% of the normal weight, while the best will be given 180% of the normal weight.

Policies and Grades (cont.) Collaboration in the sense of discussions is allowed. You should write final solutions and understand them fully. Violation of this norm will be considered cheating, and will be taken into account accordingly. Can work alone or in teams of up to 2 (two) You can also consult additional books and references but not copy from them.

Policies and Grades (cont.) Required homework will be due as specified, at the course mailbox. Late homework will be accepted up to one week after the due date, will receive a maximum grade of 80% and loose 10% for each delay day after the first one. However, bonus problems must be handed in on their due date.

Additional Information There are really 2 sub-course in the course: Basis robotics (K, IK, some D) Robot Motion Planning and navigation Evaluation of sub-courses: HW + BR: final RMP&N: a project involving actual implementation

Robot Examples

Home Robotics

A Brief History of Robotics The word robot introduced by Czech playwright Karel Capek: robots are machines which resemble people but work tirelessly. His view is still to be fulfilled! Best soccer player ever Best robot player ever

A Brief History of Robotics II Definition: a robot is a software-controllable mechanical device that uses sensors to guide one or more end-effectors through programmed motions in a workspace in order to manipulate physical objects. Today’s robots are not androids built to impersonate humans. Manipulators are anthropomorphic in the sense that they are patterned after the human arm. Industrial robots: robotic arms or manipulators

History of Robotics (cont.) Early work at end of WWII for handling radioactive materials: Teleoperation. Computer numerically controlled machine tools for low-volume, high-performance AC parts Unimation (61): built first robot in a GM plant. The machine is programmable. Robots were then improved with sensing: force sensing, rudimentary vision.

History of Robotics (cont.) Two famous robots: Puma. (Programmable Universal Machine for Assembly). ‘78. SCARA. (Selective Compliant Articulated Robot Assembly). ‘79. In the ‘80 efforts to improve performance: feedback control + redesign. Research dedicated to basic topics. Arms got flexible. ‘90: modifiable robots for assembly. Mobile autonomous robots. Vision controlled robots. Walking robots.

Robots Today Thanks to progress in mechanics, electronics, batteries and computer power, robots are becoming more visible in everyday life You can find exciting robotics projects at the Intelligent Systems Lab

The Course at a Glimpse: Kinematics F(robot variables) = world coordinates x = x(1,, n) y = y(1,, n) z = z(1,, n) In a serial robot, Kinematics is a single-valued mapping. “Easy” to compute.

Kinematics: Example 1= , 2=r 1 r  4.5 0   50o r x = r cos  y = r sin  workspace

Inverse Kinematics G(world coordinates) = robot variables 1 = 1(x,y,z) N = N(x,y,z) The inverse problem has a lot of geometrical difficulties Inversion may not be unique!

Inverse Kinematics: Example 2 1 Make unique by constraining angles

Trajectory Planning Get from (xo, yo, zo) to (xf, yf, zf) In robot coordinates: o  f Planning in robot coordinates is easier, but we loose visualization. Additional constraints may be desirable: smoothness dynamic limitations obstacles