Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints - ICCAS2019
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The document presents a quantitative measure for evaluating caging grasps with both geometrical and mechanical constraints in robotic manipulation. It emphasizes the importance of robustness in manipulation, defining caging conditions, and analyzing the factors that affect an object's escape from mechanical confinement. The study demonstrates ways to assess the effectiveness of caging grasps and the interplay between geometrical constraints and mechanical effects.
![Robustness of manipulation
How large external disturbances can the
manipulated object resist without changing its
motion?
[Similar approaches]
Y. Maeda and T. Arai: A quantitative
stability measure for graspless
manipulation, ICRA 2002.
X. Zhang et al.: Robustness of Power
Grasp, ICRA1994
pushing
Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita
11](https://image.slidesharecdn.com/iccas2019caging-qualityslideshare-191028023651/85/Homogeneous-Quantitative-Measure-of-Caging-Grasps-with-both-Geometrical-and-Mechanical-Constraints-ICCAS2019-11-320.jpg)
Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints - ICCAS2019
- 1. https://www.slideshare.net/SatoshiMakita/ This work was supported by JSPS KAKENHI Grant Number JP17H04699. Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints *S. Makita (Nat’l Inst. of Tech, Sasebo Coll.) K. Makihara (Univ. of Tsukuba) Summary Robustness of manipulation can be used to evaluate geometrical constraint
- 2. Objective To evaluate quality of both mechanical and geometrical constraints simultaneously 𝑥 𝑦 𝑃1𝑃2 𝑥 𝑦 𝑃1𝑃2 Gravity <NOT force closure> <Controllable force closure> Which situation is reliable? Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 2
- 3. Caging = Geometrical constraint Robots surround an object to confine it The object can move only within the robotic cage S. Makita and W. Wan: A survey of robotic caging and its applications, Advanced Robotics, 2017. Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 3
- 4. Partial caging = incomplete constraint The object can escape through the gap of robots Easy to enter Difficult to escape Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita The shape of gate affects difficulty of escaping 4
- 5. Quality measure based ONLY on geometrical parameters Robots as obstacles Easy to enter Difficult to escape ＜complexity of escape path＞＜difficulty to escape＞ Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 5
- 6. Not only geometrical constraint, but also mechanical effect Need energy to escape Mahler et al.: Energy-Bounded Planar Caging IEEE Trans. on Automation Science and Engineering, 2018. 𝒇 Gravitational force prevents the object from escaping S. Makita et al.: Geometrical constraint in Graping, IROS2012 Workshop: Beyond Robot Grasping - Modern Approaches for Learning Dynamic Manipulation, Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 6
- 7. Geometrical constraint and mechanical effect How large energy is required to escape? -> Necessary to define “caging” and “not caging” 𝒇 Not caging caging Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 7
- 8. Proposed idea Escapability -> mobility 𝑥 𝑦 𝑥 𝑦 gravity 𝑥 𝑦 × × Easy to move Difficult to move Infeasible to move Note: Euclidean motion (single rotation) only Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 8
- 9. Objective Evaluate quality of (partial) caging grasps for safe manipulation ＜Proposed idea＞ Apply robustness measure in robotic grasping and manipulation pushing 𝑥 𝑦 𝑃1𝑃2 𝑥 𝑦 𝑃1𝑃2 Gravity <NOT force closure> <Controllable force closure> Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 9
- 10. Assumptions for modeling • All the objects, robots are rigid bodies • All the contacts are approximated by finite contact points with friction • Coulomb friction model is adopted • All the robotic fingers are in hybrid control to bound gripping forces Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 10
- 11. Robustness of manipulation How large external disturbances can the manipulated object resist without changing its motion? [Similar approaches] Y. Maeda and T. Arai: A quantitative stability measure for graspless manipulation, ICRA 2002. X. Zhang et al.: Robustness of Power Grasp, ICRA1994 pushing Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 11
- 12. Force equilibrium against an external wrench 𝑧 = min 𝑖 𝑧𝑖 𝑧𝑖 = max 𝜁,𝒌,𝑩,𝑺,𝝉 𝜁 subject to 𝜁 𝑹1/2 −1 𝒍𝑖 + 𝑸known + 𝑾𝑪𝒌 = 𝟎 𝑱 𝑇 𝑪𝒌 − 𝝉 = 𝟎 𝑻 𝑇 𝑰3𝑀 − 𝑩 𝑪𝒌 = 𝟎 𝑺𝑻 𝑇 𝑪𝒌 ≤ 𝟎 𝟎 ≤ 𝝉 ≤ 𝜏max 𝟏 𝒌 ≥ 𝟎 𝜁 ≥ 0 The weakest direction The upper bound for each direction Force Equilibrium Joint torques and contact forces Contact points without friction Constraint on static friction Each range of joint torque Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 12
- 13. Robustness as geometrical constraint The force equilibrium in geometrical constraint is broken by infinite external forces 𝑥 𝑦 𝑃1𝑃2 𝑥 𝑦 𝑃1𝑃2 Gravity 2𝜇𝑓𝑛 − 𝑚𝑔 2𝜇𝑓𝑛 + 𝑚𝑔 𝑓𝑛 𝑓𝑛 𝜇𝑚𝑔 𝑚𝑔 +∞ 𝜇𝑚𝑔 Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 13
- 14. Numerical examples • Assumptions • The mass of the object: 1， • The mass distribution is uniform • The coefficient of static friction: 0.3 • Direction of external wrench: 14 𝒍𝑖 = ±1, 0, 0 𝑇 , 0, ±1, 0 𝑇 , 0, 0, ±1 𝑇 , 1 3 ±1, ±1, ±1 𝑇 • Gravitational force 𝑸known = 0, −9.8, 0 𝑇 • Upper bound of joint torque: 𝜏max = 40.0 𝑥 𝑦 𝑃1 𝑃4𝑃2 𝑃3 Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 14
- 15. Quality of (partial) caging grasps Arrange a finger on the bottom of the object in order to support it against the gravitational force 𝑥 𝑦 𝑃4𝑃2 𝑥 𝑦 𝑃1 𝑃3 Robustness=10.17 Robustness=12.99 Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 15
- 16. Quality of (partial) caging grasps Three-finger grasps 𝑥 𝑦 𝑃4𝑃2 𝑃3 𝑥 𝑦 𝑃1 𝑃2 𝑃3 𝑥 𝑦 𝑃1 𝑃4𝑃2 Robustness=10.17 Robustness=12.99 Robustness=24.23 Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 16
- 17. Quality of caging grasps The score for complete caging reaches its upper bound 𝑥 𝑦 𝑃1 𝑃4𝑃2 𝑃3 Robustness=52.16 Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 17
- 18. Grasp posture considering geometrical constraint Grasping a T-shaped object Support the object passively without actuating 𝑃21 𝑃22 𝑃11 𝑃12 gripper object 𝑥 𝑦 𝑃21 𝑃22 𝑃11 𝑃12 gripper object 𝑥 𝑦 minimum robustness=6.42 minimum robustness=15.08 Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 18
- 19. Conclusion • Quantitative measure of caging grasps • Robustness of manipulation -> Difficulty of moving of object (difficulty of escaping) • Evaluate the quality of geometrical constraint and mechanical effect simultaneously Manipulation planning with considering geometrical constraint Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 19
- 20. Extra slides Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 20
- 21. Objective Each grasp force is same, but the left gives us safety Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 21
- 22. Usefulness of proposed method Evaluate effect of geometrical constraint that is not related to force closure -> reliability 𝑥 𝑦 𝑥 𝑦 robustness=10.17 robustness=24.23 Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 22
- 23. Quality of partial caging (1) The shape of the gate affects difficulty of escaping S. Makita and K. Nagata: Quality of Partial Caging by a Planar Two-Fingered Hand, Advanced Robotics, 2016. Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 23
- 24. Quality of partial caging (2) It is difficult to find escape paths in the complicated workspace Makapunyo et. al: Partial Cage Quality based on Probabilistic Motion Planning, ICRA2013 Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 24
- 25. Assumptions for modeling Coulomb friction model Friction cone Range of normal force and frictional force Approximation with a convex for linearization Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 25
- 26. Assumptions for modeling Position controlled robots are often employed in caging → Excessive internal forces may be applied Position-force hybrid control to bound gripping forces 𝑥 𝑦 Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 26
- 27. Constraint on the combination of static frictional forces Constraint on motion of infinitesimal sliding Virtual sliding Friction force Valid friction forcesInvalid friction forces Selection matrix 1. T. Omata: Rigid Body Analysis of Power Grasps: Bounds of the Indeterminate Grasp Force, ICRA2001 2. Y. Maeda et al.: Analysis of indeterminate contact forces in robotic grasping and contact tasks, IROS2007 Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 27
- 28. Selection of contact points for constraint on static friction Some contact points does not slide according to motion of whole rigid body P1 P2 P3 Selection matrix Constraint on static friction with selected contact points -> Calculation with all the combinations Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 28
- 29. Robustness as geometrical constraint • Geometrical constraint (infinite robustness) • −𝑥：The object cannot move towards the robot fingers • −𝑧：The object cannot move towards the flat plane • Interference by forces • +𝑥：Static friction prevents the object from sliding • +𝑧：The gravitational force prevents the object from moving 𝑥𝑦 𝑧 Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 29
- 30. Why partial (incomplete) caging? Complete caging is not easy ＜lack of number of robots＞ ＜lack of degrees of freedom＞ Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 30
- 31. Evaluate effect of geometrical constraint Both have same value of minimum robustness 𝑥 𝑦 𝑃4𝑃2 𝑃3 𝑥 𝑦 𝑃4𝑃2 Robustness=10.17 Robustness=10.17 the object cannot move upward Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 31
- 32. Evaluate effect of geometrical constraint Amount of robustness for all the direction 𝑥 𝑦 𝑃4𝑃2 𝑃3 𝑥 𝑦 𝑃4𝑃2 Amount of Robustness for all the direction =290.5 Amount of Robustness for all the direction =404.6 Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 32
- 33. Controllable vs. without control 𝑥 𝑦 𝑃1𝑃2 𝑥 𝑦 𝑃1𝑃2 Gravity Robustness=2.94 without control Robustness=10.17 Control of fingers must be needed Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 33
- 34. Grasping with focusing on geometrical constraint • Waist-type caging Grasping a constricted part makes grasp quality high 𝑃21 𝑃22 𝑃11 𝑃12 gripper object 𝑥 𝑦 𝑃21 𝑃22 𝑃11 𝑃12 gripper object 𝑥 𝑦 Robustness=58.23 Robustness=37.83 Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 34
- 35. Grasp posture considering geometrical constraint Grasping a T-shaped object in 3D scene Support the object passively without actuating minimum robustness=4.57 minimum robustness=10.87 gripper object 𝑥 𝑦 𝑧 gripper object Homogeneous Quantitative Measure of Caging Grasps with both Geometrical and Mechanical Constraints / S. Makita 35
Editor's Notes
- #2: I will talk about robustness of grasping and manipulation with focusing on geometrical constraint called as caging. The evaluation index is derived based on force analysis.
- #3: The objective of the study is to evaluate quality of both mechanical and geometrical constraints simultaneously. In these situations, the left figure represents an object on the floor, and the right figure represents pinching grasp by two robotic fingers. In the left side, the object is not in force closure, but it can keep static state without any force control. On the other hand, in the right side, the robot always have to control grasp force to maintain force closure. Our question is “Which situation is reliable?”
- #4: I talk about caging. Caging is a geometrical constraint in grasping, where robots or a robot hand surround an object to confine it. And then the object cannot escape from the robotic cage. The advantage of caging is that even position controlled robots can capture an object like these figures without any force control. In addition, caging planning can be achieved only with shape and posture parameters of the object.
- #5: However caging grasps are not always achieved completely. In this case, the number of robots is not enough to confine the object. As for this robotic gripper, it cannot capture the object completely because of parallel mechanism. As for another case, a fish trap has a gate and fishes can go through. However it is easy for the fishes to enter the trap but is difficult to escape from the trap. Thus complete geometrical constraint is not always required in some cases.
- #6: Let us consider robots surrounding objects are obstacles for the objects. The quality of such geometrical constraint can be evaluated only with geometrical parameters.
- #7: On the other hand, such incomplete constraint is not accomplished only by geometrical features but also by mechanical effect. In the left figure, this partially constrained object needs some potential energy to escape from the cage. As a similar case, the object grasped by a humanoid hand can move upward, but the gravitational force prevents the object from moving.
- #8: From these situations, we’d like to evaluate geometrical constraints and mechanical effects simultaneously for such partial caging. However it is not simple to define both state of “caging” and “not caging”.
- #9: This is our proposed idea. We focus on mobility of objects that depends on the gravitational force and contact forces from robots. When the object can easily move from the constraint by the robots, the quality of partial caging is low. When the object cannot move, the quality of caging is high or infinity. Our basic idea is that geometrical mobility of objects can be evaluated with force analyses.
- #10: The objective of the study is to evaluate quality of grasps for safe manipulation. The proposed idea is to apply robustness measure in robotic grasping and manipulation, which can be calculated from force analyses.
- #11: I will talk about our method. These are assumptions for our force analysis. For convenience to apply the method to practical situations, we adopt rigid body model and Coulomb friction. In addition, all the robotic fingers are in force-position hybrid control to bound gripping forces.
- #12: We define the robustness of manipulation as a large external disturbances that break force equilibrium for the object. Lower external disturbances do not change the state or motion of the object.
- #13: Considering external wrench in several directions, each robustness of the object for maintaining force equilibrium is calculated with this linear programming problem.
- #14: These are simple cases of calculated robustness. In the left figure, the object cannot move downward because of the floor, and the robustness in this direction reaches infinity. It means that the force equilibrium in this direction is broken by infinite external forces. Robustness in other directions has each upper bound. In this way with the robustness measure we can evaluate the difficulty of escaping from the robotic cage.
- #15: We show some numerical examples. Although these cases are for planar object and very simple, but our proposed method can be applied to three dimensional scenes as described in our manuscript.
- #16: Let us consider a case where a two-fingered robotic hand pinches a square object. In these cases, it is preferable to arrange a finger on the bottom of the object in order to support it against the gravitational force. It is because the gravitational force facilitates the object to move along the direction of the gravitational force.
- #17: As for three-finger grasp, arranging a finger on the bottom of the object as geometrical constraint contributes to difficulty of escaping for the object.
- #18: As mentioned above, the score of robustness for complete caging reaches its upper bound. When the robotic fingers are in position control, the score reaches infinity.
- #19: These cases represent situations of grasping a T-shaped object, and the difference between these figures is posture of the object. Considering geometrical constraint, the object in the right figure is supported by the gripper. In this case, the gripper does not need any actuation to support the object, and it can be achieved passively. On the other hand, the gripper in the left figure is always required to maintain force closure grasp with actuation.
- #20: I summarize my talk. We propose a quantitative measure of caging grasps. We have to consider not only geometrical constraint but also mechanical effect to the object. Our proposed idea is based on the analysis of robustness of manipulation. The grasped object is interfered by the gravitational force and contact forces from the robotic fingers, and it is prevented from moving. Such difficulty of moving of the object represents difficulty of escaping from the robotic cage as geometrical constraints. In future works, we apply the evaluation to manipulation planning for safe manipulation.