An inverse kinematics architecture enforcing an arbitrary number of strict priority levels

By P. Baerlocher, R. Boulic. The Visual Computer, 2004

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Spatial reasoning for human robot interaction (2007, methodology): “The general formulation[17] of Generalized Inverse Kinematics with two tasks can be expressed as: ∆θ = J+λ11 ∆x1 + [J2PN(J1)] +λ2(∆x2 − J2(J+λ11 ∆x1)) where J1 and J2 are the Jacobian matrixes of two tasks, +λ1 is the singularity robust pseudoinverse operator, ∆x1 and ∆x2 are goal points for two…”
3D skeleton-based human action classification: A survey (2016, background): “Motion retargeting generates the parameters of the motion for the target character by satisfying constraints about the resulting poses (such as speci ﬁ c con ﬁ gurations of the joints' angles [94] or speci ﬁ c properties of the generated motion [95,96]).”
A Developmental Roadmap for Learning by Imitation in Robots (2007, methodology): “A very good intuitive explanation of this equation is given in [ 36 ].”
Hierarchical implicit surface joint limits for human body tracking (2005, methodology): “This extends naturally to additional constraints with higher levels of priority, but additional care must be taken when constructing the projectors [1].”
Hierarchical quadratic programming: Fast online humanoid-robot motion generation (2014, methodology): “When only equalities are set, the method comes back to the classical stat-of-the-art solutions [Hanafusa et al., 1981, Siciliano and Slotine, 1991, Baerlocher and Boulic, 2004] but is up to ten times faster.”