Module 4 Path Planning, Navigation _Robotics

Path Planning

1. Fundamentals of Robotics and Applications Department of Robotics & Automation JSS Academy of Technical Education, Bangalore-560060 (Course Code: BRA301)

2. Books S.R. Deb, Robotics Technology and flexible automation, Tata McGraw-Hill Education, 2009. Mikell P. Groover et al., "Industrial Robots - Technology, Programming and Applications", McGraw Hill, Special Edition, (2012). Ganesh S Hegde, “A textbook on Industrial Robotics”, University Science Press, 3rd edition, 2017. Reference Richard D Klafter , Thomas A Chmielewski, Michael Negin , "Robotics Engineering – An Integrated Approach", Eastern Economy Edition, Prentice Hall of India Pvt. Ltd., 2006. Fu K S, Gonzalez R C, Lee C.S.G, "Robotics: Control, Sensing, Vision and Intelligence", McGraw Hill, 1987. Further Learning https://www.robots.com/applications

3. Continuous Internal Evaluation (CIE) Assignment Component = 25 Marks Internal Assessment (IA) component = 25 Marks Two IA Tests, each of 25 Marks Two assignments each of 25 Marks For the course, CIE marks will be based on a scaled-down sum of two tests and other assessment methods. The minimum passing mark for the CIE is 40% of the maximum marks (20 marks out of 50)

4. Semester End Examination(SEE) The question paper shall be set for 100 marks. The duration of SEE is 03 hours. The question paper will have 10 questions . 2 questions per module . Each question is set for 20 marks . The students have to answer 5 full questions , selecting one full question from each module. The student has to answer for 100 marks and marks scored out of 100 shall be proportionally reduced to 50 marks . SEE minimum passing mark is 35% of the maximum marks (18 out of 50 marks). Students should secure a minimum of 40% (40 marks out of 100) in the sum total of the CIE and SEE taken together.

5. Fundamentals of Robotics & Applications MODULE 4: PATH PLANNING

6. Course outcomes (COs) (Course Skill Set) CO3: Know about various path planning techniques and analyse different motions of the robotics system At the end of the course, students will be able to,

7. MODULE 4: PATH PLANNING Definition-Joint space technique Use of P-degree polynomial-Cubic P olynomial- Cartesian space technique P arametric descriptions S traight line and circular paths P osition and Orientation planning. Content

8. PATH PLANNING

9. PATH PLANNING An industrial robot to follow a pre-planned path (trajectory planning) is the largest problem of motion. In trajectory planning, the object has to be moved in accordance with a planned trajectory . The goal of the trajectory planning is to describe the required motion as a time sequence of joint-link end effector locations and their higher order derivatives . Trajectories are generated by interpolation or approximation by properly fitting a polynomial function. The trajectory planning serves as giving reference inputs or control set points to the robot’s control system. The control system , in turn, assures that the robot executes the planned trajectories .

10. PATH PLANNING In trajectory planning, the object has to be moved from the start (initial) point to a final (end) point ; The movement has to be in accordance with the planned trajectory. When there are no obstacle in the path , the robot can have its own trajectory by which the object can be moved. It can be a straight line path or curved one which has constraints on the robot’s joints . If there are some obstacles on robot path , the robot cannot be moved in any direction . This has to be in accordance with a specific path already planned. The start positions , orientations , linear velocities , accelerations and finally the end positions are to be in line with the planned path .

11. Forward kinematics is the study of position and orientation of robot arm (tool, gripper or end effector) with respect to a reference coordinate system (robot base) with joint variables and arm parameters . Denavit-Hartenberg (D-H) method provides algorithms, result in matrix method to derive the forward kinematics solutions for robot manipulators. A real-time software is then used to compute the corresponding variables PATH PLANNING Another set of real-time software to compute the joint-based controllers is called the inverse kinematics This gives the desired position and orientation of the robot arm. Computation of inverse kinematics of robot manipulators = difficult task, because of unavoidable nonlinearities and multiple solutions.

12. With the background of the forward and inverse kinematics , when there is no obstacle in the workspace , the following two methods can be considered in path planning: Cartesian space technique Joint space technique PATH PLANNING

13. Cartesian space technique, also known as Cartesian motion planning . Is a method used in robotics for path planning and control. It involves specifying the trajectory of a robot's end-effector in Cartesian coordinates (x, y, z) rather than joint coordinates (angles or positions of individual joints). This approach is particularly useful for robots with multiple degrees of freedom and complex kinematics , such as robotic arms used in manufacturing, assembly lines, or surgery. PATH PLANNING Cartesian space technique

14. Cartesian space technique, also known as Cartesian motion planning . Is a method used in robotics for path planning and control. It involves specifying the trajectory of a robot's end-effector in Cartesian coordinates (x, y, z) rather than joint coordinates (angles or positions of individual joints). This approach is particularly useful for robots with multiple degrees of freedom and complex kinematics , such as robotic arms used in manufacturing, assembly lines, or surgery. PATH PLANNING Cartesian space technique

15. Cartesian space can be easily visualized. Cartesian space requires two-time inverse kinematics – one at the start point and the other at the endpoint. This is required for a one-stage trajectory. Cartesian space approach requires a large look-up table to store the data which may be huge for a quality path. If data can be computed using inverse kinematics in real-time, the robot’s working efficiency can be greatly affected. PATH PLANNING Cartesian space technique

16. Joint space is the second path planning which requires many-time applications of inverse kinematics. One-stage trajectory requires the applications of inverse kinematics many times . For example, after using the inverse kinematics to determine the initial and final joint positions , the robot inverse kinematics is not required again. The path can then be easily planned in the joint space. Care must be taken to see that the path does not have discontinuity. PATH PLANNING Joint space technique

17. TRAJECTORY PLANNING TERMINOLOGIES 1. Path A path is a locus of points to be traversed by the robot in executing the specified task. A path should have at least two points – the start and end points along with proper orientations 2. Trajectory A trajectory is a path with specified qualities of motion , that is, a path on which a time is specified in terms of start position , orientation , velocity , acceleration and finish point specified 3. Via points Via (path) points are the set of intermediate locations between the start point and the endpoint . The robot is expected to pass through these points to reach the endpoint.

18. TRAJECTORY PLANNING TERMINOLOGIES 4. Spline This is a smooth time function that passes through the set of path points 5. Joint space trajectory planning In this planning, each via point is specified in joint space in terms of position and orientation of the end-effector frame relative to a base frame. Each of these points is converted to a set of desired joint positions by application of inverse kinematics . A smooth time function is then determined for each joint when a robot passes through these points 6. Path update rate It is the rate at which the trajectory points are computed . This rate will indicate the next point the robot has to move

19. TRAJECTORY PLANNING TERMINOLOGIES 8. Trajectory generation Involves computing the trajectories as a time sequence of values in real-time , using a trajectory planning algorithm. This algorithm takes care of spatial and temporal constraints 7. Cartesian space trajectory planning In this planning, the path is explicitly given in Cartesian space . The path constraints (start positions, orientations, velocities, accelerations and endpoints) are specified in Cartesian coordinates. Later, these constraints can be represented in joint space through inverse kinematics

20. STEPS IN TRAJECTORY PLANNING There are three steps in trajectory planning . All of them, are required to solve the trajectory planning problem Task description Employing a trajectory planning technique Computing the trajectory

21. STEPS IN TRAJECTORY PLANNING Task description This is the first step in the motion planning problem This task can be grouped into the following three different categories The first category is the pick and place application. The task is specified as initial and final end-effector locations . No particular specification on intermediate location of end effector is given. The planner is free to formulate any convenient path. The user specifies a end point for an initial point , both points are known in Cartesian space .

22. STEPS IN TRAJECTORY PLANNING Task description This is the first step in the motion planning problem This task can be grouped into the following three different categories In the second category, in addition, to the start and end points , a specific path is to be traced by the end effector in Cartesian space. This is known as continuous path motion and continuous trajectory. For example, in arc welding , the arc welder specifies the type and parameters of the path to be traced

23. STEPS IN TRAJECTORY PLANNING Task description This is the first step in the motion planning problem This task can be grouped into the following three different categories The third category of task description is where more than one set of points are specified. For example, a pick-and-place operation in a place where obstacles are present . The first point is called the initial point while the last point is called the end point . The intermediate locations are via points. The task performed by the tool or gripper in the point-to-point motion along the continuous path motion is not part of trajectory planning .

24. STEPS IN TRAJECTORY PLANNING 2. Employing a trajectory planning technique Various trajectory planning techniques fall into one of two categories; Joint space technique Cartesian space technique. We shall consider the Cartesian space technique . In terms of point-to-point motion, with or without path points, Cartesian space techniques are employed. By adopting inverse kinematics , joint variables and their derivatives can be obtained.

25. STEPS IN TRAJECTORY PLANNING 3. Computing the trajectory The final step is to compute the time sequence values and their derivatives attained by any function generated by trajectory planning techniques . These values are computed at a particular path update . The path update rate in real-time lies between 20 and 200 Hz in a typical industrial robot system.

26. Comparison Between Cartesian Space and Joint Space Trajectories

27. Position planning focuses on determining the appropriate coordinates in space where the robot's end-effector or body frame needs to be located to perform a task effectively. This involves specifying the desired Cartesian coordinates (x, y, z) relative to a reference frame or the robot's base frame. Position planning is essential for tasks such as reaching, grasping, placing objects , or navigating through environments. Techniques for position planning include geometric methods , such as inverse kinematics , where the desired end-effector position is used to calculate the joint angles required to achieve that position. Optimization algorithms can also be employed to find optimal positions considering factors like obstacle avoidance, workspace constraints , or minimizing energy consumption . Position Planning

28. Position Planning

29. Orientation planning involves determining the appropriate orientation (rotation) of the robot's end-effector or body frame to achieve the desired alignment or orientation relative to the task or environment. This is crucial for tasks such as manipulation , assembly , or inspection , where the orientation of the end-effector significantly affects task performance . Techniques for orientation planning include methods based on Euler angles, quaternions , or rotation matrices to represent and manipulate orientations in three-dimensional space. Task-specific requirements , such as ensuring a tool is properly aligned with a workpiece or maintaining a specific orientation relative to gravity, drive the orientation planning process. Constraints such as avoiding singularities ( configurations where the robot loses degrees of freedom) or optimizing for stability and dexterity may also influence orientation planning. Orientation Planning

30. Use of P-degree Polynomial P-degree polynomial" refers to a polynomial of degree of P. Where P is a chosen degree determined by the specific requirements of the robot's motion or trajectory. Example, in path planning, a higher-degree polynomial might provide smoother paths but, also introduce more computational complexity. Engineers and researchers might use polynomials of different degrees depending on factors such as the desired smoothness of the trajectory , computational efficiency , and physical constraints of the robot .

31. Use of P-degree Polynomial Use of a p-degree (p = 3) polynomial as the interpolation function when a set of path points is given. For a smooth motion between two points, the selection of a single polynomial for entire joint path depends on the number of constraints such as; initial position initial velocity final position final velocity

32. Use of P-degree Polynomial The expression represents a polynomial trajectory or curve in terms of time t. Where a i , i = 0, 1, 2 and 3 are four coefficients, related by their constraints. Determining the shape and behaviour of the trajectory. This polynomial is commonly used in robotics for trajectory planning and control. Each coefficient a i ​ affects different aspects of the trajectory: a ​ determines the initial position or offset. a 1 ​ determines the initial velocity or slope at the start of the trajectory . a 2 influences the acceleration or curvature of the trajectory. a 3 ​ affects the jerk, which is the rate of change of acceleration.

33. Use of P-degree Polynomial Specifying start and finish points is not enough for satisfactory performance. While picking up an object , the motion of the end effector must be directed away from the supporting surface of the object to avoid crashing of the end effector with the supporting surface. Thus, a ‘ lift-off position ’ along with outward normal away from the surface has to be considered . Based on similar consideration, a ‘set-down position ’ is selected to specify the smooth and correct approach, which gives the following four position constraints: ( i ) Initial position (ii) Lift-off position (iii) Set-down position (iv) Final position. Example: simple pick and place task

34. Use of P-degree Polynomial The robot begins moving at constant acceleration , away from an initial position in an appropriate direction, in a vertically upward direction from a horizontal surface , the initial position is complete. After it has moved to a safe distance , lift-off is complete . From then onwards, it moves at a constant velocity with zero acceleration. This constant velocity and zero acceleration motion continue until it reaches the set-down position. From this point it begins to vertically decelerate reaching the final position. Figure illustrates this trajectory. This is known as a linear function with parabolic blends (LFPB) and has six constraints – four as listed above , one acceleration constraint in the beginning and one deceleration constraint in the final stage. Example: simple pick and place task Position, Velocity and Acceleration Profiles

35. End