Robot Path Planning

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## Robot Path Planning

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**Robot Path Planning**CONTENTS 1. Introduction 2. Interpolation path planning, 2003/2004 winter**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**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**Robot Path Planning**Cubic polynomials: There are at least four conditions to constrain the interpolation: (1) (2) (3) (4) path planning, 2003/2004 winter**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**Robot Path Planning**(6) path planning, 2003/2004 winter**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**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**Robot Path Planning**Figure 2 shows the position Velocity Acceleration path planning, 2003/2004 winter**Robot Path Planning**Figure 2 path planning, 2003/2004 winter**Robot Path Planning**Cubic polynomials for a path with via points In this case path planning, 2003/2004 winter**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**Robot Path Planning**Figure 3 path planning, 2003/2004 winter**Figure 4**Constant Velocity Improvement Robot Path Planning Linear function with parabolic blends path planning, 2003/2004 winter**Robot Path Planning**Change slope path planning, 2003/2004 winter