Least squares quadratic optimization library for Robotics.
This library contains a solver using a stack-of-tasks1,2 approach for finding solutions to a set of weighted least-squares problems with a hierarchical structure. For every hierarchy, the solver finds a solution to the following least squares optimization problem:
subject to:
where
,
,
and
are the weight, coefficient matrix, and bias of the
-th
task, respectively; and
,
,
and
are the coefficient matrix, lower bound, and upper bound for the
-th
constraint, respectively.
The tasks of each hierarchy are projected to the remaining hierarchies as a nullspace projection constraint of the form:
where
contains the stacked coefficient matrices of the tasks in the previous
hierarchy, and
is the solution to the optimization problem of the previous hierarchy.
- N. Mansard, O. Stasse, P. Evrard and A. Kheddar, "A versatile Generalized Inverted Kinematics implementation for collaborative working humanoid robots: The Stack Of Tasks," 2009 International Conference on Advanced Robotics, Munich, 2009, pp. 1-6.
- A. Rocchi, E. M. Hoffman, D. G. Caldwell, and N. G. Tsagarakis, “Opensot: a whole-body control library for the compliant humanoid robot coman,” in Robotics and Automation (ICRA), 2015 IEEE International Conference on. IEEE, 2015, pp. 1093–1099.