@Article{dimitrov:rsj:2014,
  author    = {Dimitrov, Dimitar and Wieber, Pierre-Brice and Escande, Adrien},
  title     = {Multi-objective control of robots},
  journal   = {Journal of the Robotics Society of Japan},
  year      = {2014},
  volume    = {32},
  number    = {6},
  pages     = {512--518},
  doi       = {https://doi.org/10.7210/jrsj.32.512},
  url       = {https://drdv.github.io/pdf/rsj14.pdf},
  keywords  = {Lexicographic Optimization, Task Prioritization, Hierarchical Problems, Inequality Constraints},
  abstract  = {Even though over 20 years old, the above quote still reflects well a common practice in the field of robotics. That is, not establishing a clear separation between: (i) what one wants to achieve, and (ii) how this must be done. Using high-level goals for posing real-world problems in mathematical terms can be advantageous since, at the level of modeling, one need not consider the particular technique for approaching their solution. In fact, being able to abstract the problem formulation can be viewed as a part of the revolutionary development that followed the birth of the field of linear programming [1], because practitioners could be trained to cast situations (of potentially great complexity) in terms of a set of general goals and rely on available solvers developed by specialists in the fields of numerical analysis and optimization. Such separation leads to a reliable solution process. In this note we argue that the ability to define typical robotic problems in terms of lucid goals is beneficial not only from the point of view of clarity of presentation, but also for efficiency of computations. Our main point is that this can be achieved through the explicit use of multi-objective formulations. By means of several examples, we illustrate the advantages of this modeling approach and suggest that, by leveraging standard tools from the field of multi-objective optimization, such formulations can be resolved reliably and efficiently. We summarize some recent developments of (the already classical in the field of robotics) task prioritization, among which the fact that hierarchical problems can be interpreted as a particular type of multi-objective models.},
  publisher = {The Robotics Society of Japan},
  address   = {Bunkyo-Ku Hongo 2-19-7 Blue Bulding 2F 1130033, Tokyo, Japan}
}