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EXPERIMENTS

We tested each simulation with a (unrealistically) high coefficient of friction (μ = 100) and “infinite” friction (μ = 10⁸). Ideally, we would have only assessed the infinite friction case (allowing us to remove normal slip due to Coulomb friction as a point of faiure), but we were concerned that the inclusion of the friction coefficient in the LCP matrix (see for this matrix) could affect numerical stability on the direct LCP solvers.

The experimental controls consisted of each of the three simulators (four in the case of the multi-block experiment) listed previously using GAZEBO’s default parameters. While we believe that it is possible to improve on these parameters significantly for this task, we wished to establish a baseline of performance. GAZEBO’s default parameters have been determined using domain knowledge to maximize performance (speed and accuracy) over numerous simulation models and environments.

The experimental controls used realistic inertial values for all simulated models and primitive geometric boxes to model the grippers and grasped objects.

Addendum: We followed up the initial experimentation with an additional run of the ode trials using a tuned set of parameters. The results have been updated to reflect both the 'default' ode performance and the 'tuned' ode performance.

Industrial robot grasping examples

To assess multiple points of comparison, we varied the collision geometry of both the grippers and the grasped object, and we varied the inertial properties of the arm. An overview of the experimentation performed with the industrial arm is described on the Overview page and the results are detailed on the Industrial Arm Grasping page.

Varying geometric types

In addition to the establishing performance for the experimental controls that used only primitive geometric types, we ran experiments where we substituted polygonal collision meshes for contacting surfaces. This battery of experiments included substituting a tessellated mesh for the grasped object, substituting a tessellated mesh for the grippers, and substituting tessellated meshes for both the grippers and the grasped object. We wished to test the hypothesis that triangle-mesh based geometries could cause contact data to be determined incorrectly, thereby causing grasp failure.

Varying inertial properties

We ran an experiment that varied the inertial properties of the links of the robot arm (where present) and gripper. We assigned the shoulder link a mass of 1kg and inertia matrix of identity. Each subsequent link in the chain would have its inertial properties scaled geometrically (i.e., the second link would be scaled by 1/x, the third link would be scaled by 1/x², etc.) We experimented with scaling factors between 1.0 and 10.0. This experiment aimed to test the hypothesis that better or worse conditioning of the manipulator inertia matrix^† could improve or worsen grasping performance. We based this hypothesis on work of Featherstone (1) that showed that the condition number of this matrix grows up to O(n⁴) in the number of links in a robot and is also dependent on variations in link inertia (among other factors).

Multiple block grasping example

The multiple block grasping experiment was assessed on differing numbers of blocks (one to eleven) in the grasp. The hypothesis behind this experiment is that more blocks require more iterations in the iterative solvers to sustain grasping. It is well known that numerical robustness of pivoting solvers decreases with increasing numbers of variables: rounding errors from the pivoting errors accumulate and can cause failure. Varying the number of blocks should demonstrate points of failures in the two solvers. An overview of the experimentation performed with the multiblock gripper is described on the Overview page and the results are detailed on the Multiple Block Grasping page.

† Although such a matrix is not explicitly constructed within most of these simulators, the conditioning of that matrix should yield a measure of numerical stability.

REFERENCES

Featherstone R., "An empirical study of the joint space inertia matrix", The International Journal of Robotics Research, 2004

================ Industrial Arm Grasping Experiments
Multiple Block Grasping Experiments