Solver
A solver implements a mathematical method to resolve a QP/LP problem (a stack).
A solver is implemented deriving from the OpenSoT::Solver class in Solver.h implementing the virtual method solve(Vector_type& solution).
Solvers in OpenSoT library permit to set mulitple levels of hard priorities between tasks. When two or more tasks are at a soft priority, they are intended to be summed in the same cost function with a different weight, for example, given two tasks \(\mathcal{T}_1\) and \(\mathcal{T}_2\), is possible to write a cost function where both the tasks are solved together but with \(\mathcal{T}_1\) which is 10 times more important than \(\mathcal{T}_2\):
meaning that when the solver will give more importance (ten times) to \(\mathcal{T}_1\) w.r.t. \(\mathcal{T}_2\). However, if the two tasks are minimizing different quantities, they may not be scaled the same, leading to scaling issues (e.g. position in meters and orientation in radiants). Therefore, the weight 0.1 may not be enough to properly set a soft priority between the tasks.
In these cases is possible to set a hard priority, meaning that the highest priority task will be minimized regardless the less priority task. There are several techniques to enforce hard priority between tasks, for example null-space projection, which is implemented in the eHQP solver. To enforce hard-priorities between tasks using the MoT you just need to use the / operator:
where \(\mathcal{S}_1\) is a stack. Notice that the way the hard priority is implemented depends on the particular solver used. Soft and hard priorities can be mixed together and several layers can be created up to saturate the Degrees of Freedom (DoFs) of the problem:
Available Solvers
In OpenSoT, solvers are often implemented putting together 2 layers: a front-end, and a back-end. The front-end prepares the optimization problems to be solved starting from the given stack, by means of putting together the necessary matrices and vectors, computing cost fucntions and so forth. The back-end solves the optimization problem.
Not all the solvers follow this structure, for example, the HCOD solver consists just in a front-end. OpenSoT provides the following out-of-the-box solvers:
The eHQP solver for equality-only Hierarchical QPs
The iHQP solver for inequality Hierarchical QPs
The nHQP solver for null-space Hierarchical QPs
The HCOD solver for Hierarchical Complete Orthogonal Decomposition
You can find here a comparison among the different solvers.