Master Thesis

Hierarchical task control through lexicographic semidefinite programming

Work default illustration


  • Started: 15/10/2017
  • Finished: 03/10/2018


In this thesis, we present a new method to simultaneously fulfill several tasks with a robot.
We take advantage of redundant robots, in terms of degrees-of-freedom, and we are able to prioritize between tasks by expressing the control law as a lexicographic semidefinite programming, which consists on a hierarchized group of optimal problems.
These optimal problems are formulated through linear matrix inequalities, enabling the definition of equality tasks (commonly done in the literature) and also inequality tasks.
With these formulation, we describe the problem in a compact form that ease its extension.
Moreover, this structure using linear matrix inequalities allows us to use common linear algebra tools, hence to use fast specialized solvers, making feasible a real-time solution of the problem for highly redundant robots.
We express the tasks in the acceleration domain, obtaining smooth joint references.
The proposed approach is applied to autonomously drive aerial manipulators, providing the analysis of simulations and real case studies in the second part of this work.
For the sake of completeness, we also include in the appendices complete descriptions of general formulation procedures as well as a complete and didactic practical example.
The code produced within this work is made publicly available for the benefit of the community.

The work is under the scope of the following projects:

  • AEROARMS: AErial RObotics System integrating multiple ARMS and advanced manipulation capabilities for inspection and maintenance (web)
  • MdM: Unit of Excellence María de Maeztu (web)