Interactive manipulation of articulated objects with geometry awareness

Techniques for interactive 3D manipulation of articulated objects in cluttered environments should be geometrically aware, going beyond basic inverse or forward kinematics to allow contact while preventing interpenetration. This paper describes a general purpose interactive object manipulation technique using nonlinear optimization. The method converts geometry awareness into sets of inequality constraints and handles nonlinear equality and inequality constraints efficiently without restricting object topology. Our iterative algorithm has a quadratic convergence rate and each iteration can be solved in O(n_nz(L)), where n_nz(L) is the number of non-zeros in L, a Cholesky factor of a sparse matrix. To promote additional speedup, symbolic factorization is separated from numerical computation. Our approach provides a framework for using optimization techniques in interactive tools for building and manipulating models in constrained, cluttered environments