8 Grasp Force Optimization Contents

# 8 Grasp Force Optimization

The Grasp Quality Metrics that we have discussed so far only deal with forces applied at the contacts. The form-closure criterion asks whether there exists some combination of legal contact forces that add up to a certain resultant on the target object. In practice though, robotic hands are controlled by setting joint forces. The Grasp Force Optimization (GFO) problem, in a nutshell, asks the following questions: is there a combination of legal joint forces that result in the desired contact forces? If there are multiple solutions to this problem, which one is "optimal"?

GFO is an active area of research in itself, and many publications present various formulations and solvers. As a starting point, we recommend the Grasping Chapter (authored by Domenico Prattichizzio and Jeffrey C. Trinkle) in the Springer Handbook of Robotics. Here we just give a very quick overview of the GFO tools that are available in GraspIt.

The GraspIt code for performing GFO has gone through two iterations. The first one is from GraspIt release 0.9. That version was based on the beautiful mathematical formulation presented in the paper Grasp Analysis as Linear Matrix Inequality Problems, by Li Han, Jeffrey Trinkle and Zexiang Li, IEEE Transactions on Robotics and Automation, vol. 16, 1998. However, this code was not thoroughly tested and was not commented, and unfortunately has fallen into disrepair. As such, it might be removed from future releases; please contact us if you are interested in obtaining a copy of that code.

The new version is based on a different mathematical formulation, using Quadratic Programming. It has been thoroughly tested and is extremely well commented in the source code. However, you will need a Quadratic Program solver for it to work. We strongly recommend the excellent commercial solver Mosek. Student licenses are free, and the integration with GraspIt is seamless - just uncomment the appropriate line in the file graspit.pro.

## 8.1 GFO computations through the main interface

A subset of the GFO functionality is available through a simple dialog accessible from the GraspIt GUI. You can use this anytime you have a grasp - for example, load the example world file dlr_flask.xml and then click Grasp -> Auto Grasp. You can now use Grasp -> Grasp Force Optimization to access the GFO dialog.

The drop-down list allows you to choose the optimization type being performed. The main options are:

• Grasp force - GraspIt will attempt to compute the optimal joint forces so that contact forces result in a null wrench on the object.
• Compliant joint equilibrium - GraspIt will attempt to compute the contact forces that balance out a set of given joint forces, while resulting in an object wrench of the smallest possible magnitude. This case is of particular interest for underactuated hands with compliant, spring joints where not all joint forces can be set independently. See the Joint Coupling chapter for details.
• DOF force equilibrium - GraspIt will attempt to compute the contact forces that balance out a set of given DOF forces, while resulting in an object wrench of the smallest possible magnitude.

When the On button is checked, GraspIt will attempt to solve the optimization problem of the specified type each time the grasp is changed (contacts are added or broken). The dialog will inform you of the outcome of the optimization. Note that some optimization problems can be unfeasible in certain hand configurations. If the optimization is solved, GraspIt will display the computed contact forces in the dedicated space of the main window, and also visually indicate the contact forces using the same mechanism used for displaying computed contact forces during dynamic simulation (yellow arrows at each contact). Note that computed joint torques are not displayed through the GUI, but rather printed to the console.

## 8.2 GFO code and advanced details

We have found that the mathematical formulations for GFO allow for almost endless possibilities and combinations of optimization criteria vs. constraints. In general, the GFO code in GraspIt is concerned with the following aspects:

• goal is to compute contacts forces and/or joint torques
• contact forces must be legal (inside friction cones)
• contact forces must be balanced by joint torques
• resultant object wrench should have a small (or null) magnitude

In general, any 1 of these 3 goals can be made into an optimization objective, while the other 2 become constraints. You can mix and match in many ways, which is why we have not included more options inside the GUI. However, the code is really well documented and you should be able to write up your own GFO routines to match your project. The best place to start is the Grasp class, more specifically the function int Grasp::computeQuasistaticForcesAndTorques(Matrix *robotTau);. Inside this function you will find multiple options for performing the core optimization, all are documented.

Finally, as of the writing of this chapter, we have one paper in press that will detail the GFO engine. Please see the Publications section of this manual for details.