Workspace Optimization for Autonomous Mobile Manipulation

Transcription

1 for May 25, 2015 West Virginia University USA

2 1 Many tasks related to robotic space intervention, such as satellite servicing, require the ability of acting in an unstructured environment through autonomous mobile manipulation. When introducing levels of autonomy in robotic intervention, several issues appear repeatedly. The full cycle of an autonomous intervention is here presented through a case study in underwater robotics, a project called the Semi-Autonomous Underwater Vehicle for Intervention Missions 1. 1 began in 1997 at the University of Hawaii at Manoa, under Prof. Junku Yuh. The project was funded by the Office of Naval Research over a 10 year period and administered by Dr. J. Yuh, S.K Choi and G. Marani.

3 I 2 Issue 1: Target area navigation. One of the most important aspects in autonomy is the environment perception. The best solution is determined by several factors, including task and environment.

4 I 3 Issue 2: Vehicle positioning. An autonomous servicer must be capable of performing workspace, correcting the vehicle position for maximizing the manipulability of the arm during its operations.

5 I 4 Issue 3: Arm system. Cope with many issues commonly seen in robotics (kinematic singularities, collisions, joint limit, motor saturation, etc).

6 5 An autonomous robotic system must be able to intelligently cope all the above situations to successfully complete the given mission, whenever possible.

7 Autonomous manipulation system: I performs intervention tasks with limited human supervision; I the human operator should be able to the manipulation process with only high-level commands; I the robot determines what joint trajectories need to be followed for successfully achieving goals. 6

8 7 Resolved Motion Rate Control (RMRC) is a local method for solving inverse kinematics problems. Given a generic task r = f (q), it uses the Jacobian J of the forward kinematics to describe a change in the end-effector position: δr = f δq = J (q) δq (1) q In RMRC we compute δq for a given δr and q by solving the above linear system. The solution, in the general form, is 2 : δq = J + (q) δr + ( I n J + (q) J (q) ) y (2) where J + (q) is the Moore-Penrose pseudo-inverse of J(q), y is an arbitrary vector and I n indicates an identity matrix. 2 Y. Nakamura: Advanced Robotics: Redundancy and, Addison Wesley, 1991

9 Nakamura introduced the inverse kinematics taking into account of the priority of the subtasks: 8 Task 1 (Priority 1) Task 2 (Priority 2) r 1 = f 1 (q) r 2 = f 2 (q) Inverse kinematics with priority δq = J + 1 δr 1 + Ĵ + ( 2 δr2 J 2 J + ) ( 1 δr 1, Ĵ2 = J 2 In J + ) 1 J 1

10 Example with: Task 1 (higher priority): Cartesian position of the end-effector Task 2 (lower priority): orientation of the end-effector 9

11 10 The direct implementation of the task priority in its original form δq = J 1 + δr 1 + Ĵ + 2 ( δr2 J 2 J 1 + δr 1 ) presents difficulties due to physical and mathematical singularities: Kinematic singularities: loss of rank of J 1 and J 2. Algorithmic singularities: loss of rank of Ĵ 2 with J 1 and J 2 of full rank (3)

12 To solve the previous problem we use the concept of Task reconstruction. The basic idea in task reconstruction is to circumscribe singularities by moving, when approaching to them, on a hyper-surfaces where the distance index (measure of manipulability) remains constants. 11 Reconstructed trajectory mom = m Desired trajectory Singular Configuration mom = 0 Figure: Conceptual diagram of

13 12 Task reconstruction process Phase 1: definition of a distance index In case of singualities avoidance, the "distance from singularities" index is given by the measure of manipulability (MOM), introduced by Yoshikawa: µ (J) = det (JJ T ). (4) µ (J) takes a continuous non-negative scalar value and becomes equal to zero only when the Jacobian matrix is not full rank.

14 13 Task reconstruction process Phase 2: application 3 where: δq = J + (q) TR (J, m (q), δr) (5) TR (J, m (q), δr) = ( I m k 1 n m n m T ) δr + k 2 n m n m = ( m(q) q m(q) q J + ) T J + k 1 = 1 sign (δr n m) k m (m, m, m) ( 2 k 2 = K r k m m, m 2, m ) 2 (6) 3 Marani, G, Yuh, J., to Autonomous, Springer Tracts in Advanced Robotics

15 Task reconstruction process n m r p k r n n 1 m m Reconstructed trajectory r 14 Desired trajectory m q m q 0 m Figure: Geometric interpretation of the task reconstruction concept

16 Task reconstruction example Cartesian position has priority over orientation 15

17 TR advantages: 16

18 TR advantages: Fewer tuning parameters (mainly the distance limit) 16

19 16 TR advantages: Fewer tuning parameters (mainly the distance limit) The performance is then simply affected by the choice of the lower limit.

20 16 TR advantages: Fewer tuning parameters (mainly the distance limit) The performance is then simply affected by the choice of the lower limit. Based on a real-time evaluation of the measure of manipulability, this method does not require a preliminary knowledge of the singular configurations

21 16 TR advantages: Fewer tuning parameters (mainly the distance limit) The performance is then simply affected by the choice of the lower limit. Based on a real-time evaluation of the measure of manipulability, this method does not require a preliminary knowledge of the singular configurations Can be regarded as a dynamic priority-changing algorithm 4. 4 J. Kim, G. Marani, W. K. Chung, J. Yuh: Kinematic Singularity Avoidance for Autonomous in Underwater, The Fifth ISOPE Pacific/Asia Offshore Mechanics Symposium, Daejeon, Korea, November 17-20, 2002

22 17 With a different choice of the distance index, the TR algorithm can be applied also to: collision avoidance joint limits avoidance workspace

23 Collision avoidance Index: "minimum distance between all objects" 18

24 Joint limits avoidance. Index: n P (q) = N p (q i ), N p (q i ) = 1 i=1 ( ) 2 2 (qi q i,min ) (q i,max q i,min ) 1 Example with imposed joint limits (0, π/2) to elbow and wrist: 19

25 The whole vehicle-navigation system is regarded as unique open chain with multi-degrees of freedom joint 5 6,7,8 20 joint 1 is a 6 DOF joint joints 2 through 8 are 1 DOF rotational e 0

26 21 Goal: target optimally positioned within the dexterous arm workspace. : TR index: measure of manipulability of the whole chain Task r 1 (3 DOF): Cartesian position of Link 8 (the endeffector) Task r 2 (3 DOF): Orientation of Link 8 (the end-effector) Task r 3 (3 DOF): Position (x and y) and orientation (around z) of the vehicle (hovering condition) 5 5 In our implementation, the hovering condition is achieved by setting to zero the time derivative of the third manipulation variable

27 Result I 22 The vehicle position is autonomously changed only when needed, to increase the manipulability of the arm:

28 0.65 Measure of manipulability of J 1 (linear) mom(j 1 ) Time (sec)

29 0.4 Measure of manipulability of J 2 (angular) mom(j 2 ) Time (sec)

30 Robotic systems capable of operating autonomously in unstructured environments will need this type of complete solution strategy. Many issues appear repeatedly in autonomous robotic manipulation (of all areas): target area navigation vehicle positioning arm systems 25, Junku Yuh: to Autonomous Springer Tracts in Advanced Robotics

31 The research relative to the project was conducted at the Autonomous Systems Laboratory (University of Hawaii). It was sponsored by ONR (N , N , N , N , N ). Special thanks are given to all the people who participate to the development, including Giuseppe Casalino (DIST, University of Genoa, Italy), the Dept. of Mechanical Eng., Pohang University of Science and Technology, with Prof. Wan Kyun Chung, and Dr. Aaron Hanai of the university of Hawaii.

32 Thank you