1. Robot Path Planning CONTENTS 1. Introduction 2. Interpolation path planning, 2003/2004 winter

2. Robot Path Planning 1. Introduction • The user specifies goal points. There is an issue about the intermediate points. • Goal points are converted to joint points -> joint scheme, so the issue becomes to determine the intermediate angles given two angles as well as their time stamps (see Figure 1. • Criterion of determining these intermediate angles is: “smoothness” of eth motion. 2. Joint space schemes path planning, 2003/2004 winter

3. Robot Path Planning Given the initial and end goal points, there are different ways to interpolate, see Figure 1. Figure 1 Rotary motor path planning, 2003/2004 winter

4. Robot Path Planning Cubic polynomials: There are at least four conditions to constrain the interpolation: (1) (2) (3) (4) path planning, 2003/2004 winter

5. Robot Path Planning • These four constraints can be satisfied by a polynomial of at least third degree. A cubic has the form: (5) We can get the velocity and acceleration expression for the above equation (5). We can determine the coefficients as follows: path planning, 2003/2004 winter

6. Robot Path Planning (6) path planning, 2003/2004 winter

7. Robot Path Planning • Example: A single-link robot with a rotary joint is motionless at It is desired to move the joint in a smooth manner to in 3 seconds. Find the coefficients of a cubic which path planning, 2003/2004 winter

8. Robot Path Planning accomplishes this motion and brings the manipulator to rest at the goal. Solution can be found by plugging into the equations for the coefficients, we can find: path planning, 2003/2004 winter

9. Robot Path Planning Figure 2 shows the position Velocity Acceleration path planning, 2003/2004 winter

10. Robot Path Planning Figure 2 path planning, 2003/2004 winter

11. Robot Path Planning Cubic polynomials for a path with via points In this case path planning, 2003/2004 winter

12. Robot Path Planning Cubic polynomials for a path with via points In this case, the condition about velocity has been changed; see the previous slides The four coefficients can be found (to be filled in the classroom: (7) path planning, 2003/2004 winter

13. Robot Path Planning Figure 3 path planning, 2003/2004 winter

14. Figure 4 Constant Velocity Improvement Robot Path Planning Linear function with parabolic blends path planning, 2003/2004 winter

15. Robot Path Planning Change slope path planning, 2003/2004 winter