Multi-Objective Control of Robots

"Prior to linear programming it was not practical to explicitly state general goals and so objectives were often confused with the ground rules for the solution. (.) Thus the means to attain the objective becomes the objective in itself, which in turn spawns new ground rules as to how to go about attaining the means (.). These means in turn become confused with goals. " G. B. Dantzig 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 2014 4 16 Lexicographic Optimization, Task Prioritization, Hierarchical Problems, Inequality Constraints * 1 Rhone-Alpes, 38334 St-Ismier Cedex, France * 2 Tsukuba-shi, Ibaraki 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 prioriti-zation, among which the fact that hierarchical problems can be interpreted as a particular type of multi-objective models. 1. Multi-criteria decision making Multi-criteria decision making has been popular for many decades and a variety of optimization techniques for facilitating it has been developed. The ability to handle multiple criteria provides more expressive models , leading to an increase in flexibility and reliability of design, control, and estimation schemes. The key question in many areas is how to define what is a good/desirable behavior of a given process and often the answer involves the specification of multiple conflicting objectives. Conflicting objectives occur naturally in typical robotics problems. For example, consider a ma-nipulator arm mounted on a free-floating base. Then, due to the momentum conservation, the objective of tracking a given end-effector profile would conflict with the objective of preserving the posture of the base. Resolving conflicts between objectives usually requires the participation of a human decision-maker who can express preference relations between alternative solutions. The involvement of a decision-maker can come at different stages of the solution process. In some applications , solving a multi-objective optimization problem is defined as the generation of the pareto-optimal surface , at which point a decision-maker can analyze the results and choose the most appropriate pareto-optimal point. This technique, however, might be inadequate to the needs of other applications e.g., real-time robot