A novel method for computing the 3D friction cone using complimentary constraints

Abstract: Modeling the Coulomb Friction Cone in trajectory optimization is typically done by linearizing it along a series of vectors. Often, these vectors define the edges of polyhedral estimations of the cone. This article provides an alternate approach that samples the cone along a vector that satisfies the Maximum Dissipation Principle, which is shown to be significantly more computationally tractable. The proposed technique uses the polar representation of the relative velocity of a contact point on a surface to determine the direction of the resultant friction force and linearizes the friction cone along this vector. This study describes the development of the proposed model. Thereafter, a trajectory optimization experiment was conducted to compare the traditional four-sided polyhedral estimation of the friction cone with the novel method. Compute time and computational complexity were used as performance metrics in this study. Results from these experiments indicate that the proposed method reduced the compute time by 39.13% and a 57.00% reduction in inequality constraints when compared to the 4-sided polyhedral estimation.

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