hpp-constraints: hpp-constraints

hpp-constraints 9.0.2 Definition of basic geometric constraints for motion planning

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hpp-constraints

# 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.