Abstract: Based on the fact that nonlinear friction force limit constraints are equivalent to the positive definiteness of a certain matrix, the problem of grasping force planning for multi-fingered hand can be formulated as an optimization problem on the smooth manifold of linearly constrained positive definite matrices, and the optimal grasping force can be found by using the linear constraint gradient flow. When the number of fingers is large, high-dimensional description matrix greatly limits the calculation speed of the traditional linear constraint gradient flow. Therefore, in order to solve the problem, a grasping force vector based linear constraint gradient flow algorithm for real time applications is proposed, based on the affine constraint property of the description matrix in the optimization process. Instead of the description matrix, a grasping force vector is used to describe the linear constraint gradient flow, which greatly reduces the dimensional number and the computational cost of the linear constraint gradient flow expression. The proposed algorithm is implemented on a four-fingered dexterous hand with point friction contact model for grasping force com-putation. The influence of the weight factor and step factor on the computational result and the convergence speed is analyzed, and the correctness and real-time capacity of the proposed algo-rithm are verified.

Key words: Force optimization, Gradient flow, Linear constraint, Multi-fingered hand