Grasp Analysis as Linear Matrix Inequality Problems

Three important problems in the study of grasping and manipulation by multi-fingered robotic hands are: 1) given a grasp characterised by a set of contact points and the associated contact models, determine if the grasp has force closure; 2) if the grasp does not have force closure, determine if the fingers are able to apply a specified resultant wrench on the object; and 3) compute "optimal" contact forces if the answer to problem (2) is affirmative. In this paper, based on an early result by Buss-Hashimoto-Moore (1996), which transforms the nonlinear friction cone constraints into positive definiteness of certain symmetric matrices, we further cast the friction cone constraints into linear matrix inequalities (LMIs) and formulate all three of the problems stated above as a set of convex optimization problems involving LMIs. We perform simulation studies to show the simplicity and efficiency of the LMI formulation to the three problems.

Authors

• Li Han
• Jeffrey C. Trinkle
• Zexiang Li 0001

Keywords

• Linear matrix inequalities
• Friction
• Robot kinematics
• Grasping
• Fingers
• Constraint optimization
• Contacts
• Computer science
• Polynomials
• Educational robots
• Linear Inequalities
• Linear Matrix Inequality Problem
• Optimization Problem
• Contact Point
• Symmetric Matrix
• Study Of Problems
• Convex Optimization
• Contact Force
• Community Controls
• Contact Model
• Nonlinear Constraints
• Positive Definite
• Form Of Linear Matrix Inequalities
• Polynomial Time Complexity
• Simulation Results
• Objective Function
• Computation Time
• Feasible Set
• Normal Component
• Coulomb Friction
• Strict Inequality
• Normal Force
• Null Space
• Unit Sphere
• Symmetric Positive Definite Matrix
• Linear Inequality Constraints
• Technical Report
• Joint Effort