Article,
Dextrous hand grasping force optimization
Robotics and Automation, IEEE Transactions on, 12 (3): 406 -418 (June 1996)
DOI: 10.1109/70.499823
Abstract
A key goal in dextrous robotic hand grasping is to balance
external forces and at the same time achieve grasp stability and minimum
grasping energy by choosing an appropriate set of internal grasping
forces. Since it appears that there is no direct algebraic optimization
approach, a recursive optimization, which is adaptive for application in
a dynamic environment, is required. One key observation in this paper is
that friction force limit constraints and force balancing constraints
are equivalent to the positive definiteness of a certain matrix subject
to linear constraints. Based on this observation, we formulate the task
of grasping force optimization as an optimization problem on the smooth
manifold of linearly constrained positive definite matrices for which
there are known globally exponentially convergent solutions via gradient
flows. There are a number of versions depending on the Riemannian metric
chosen, each with its advantages, Schemes involving second derivative
information for quadratic convergence are also studied. Several forms of
constrained gradient flows are developed for point contact and
soft-finger contact friction models. The physical meaning of the cost
index used for the gradient flows is discussed in the context of
grasping force optimization. A discretized version for real-time
applicability is presented. Numerical examples demonstrate the
simplicity, the good numerical properties, and optimality of the
approach
