hpp-constraints Documentation

Mathematical Concepts

This package provides a representation of the following mathematical concepts:

• differentiable functions from a Lie group, for instance the configuration space of a robot (hpp::pinocchio::Device) to a another Lie group;
• implicit constraints are composed of a left hand side that is a differentiable function, a comparison vector, and a right hand side;
• explicit constraints are numerical constraints that can be solved by computing some input variables with respect to others.

Numerical Solvers

The constraints defined in the previous section can be solved by some numerical solvers.

• HierarchicalIterative solves a set of implicit constraints with priority order following a Newton like iterative procedure.
• BySubstitution derives from the former and substitutes output variables of explicit constraints with their explicit expression, solving numerically over the remaining variables.
• Compatible explicit constraints are gathered into ExplicitConstraintSet and used by BySubstitution solver.

One of the most common use cases of explicit constraint is the relative pose constraint where a free floating object is hold by a robot gripper. In this case, the configuration variables of the object can be explicitely expressed with respect to the robot configuration variables.