Numerical Optimization and Motion Generation in Robotics

A desired robot motion can be conveniently prescribed as a set of objectives and constraints in spaces relevant to that motion, that need to be solved to retrieve the actual configuration trajectory or the command. Numerical optimization has become a widely used tool for that purpose. Its use in robotics is heavily dependent on computational efficiency, which relies on two aspects: the formulation of the optimization problem and its resolution.
In this talk, I will present contributions to both aspects in the context of multi-contact planning and whole-body control with humanoid robots as the main contributors of use-cases. These contributions relate mostly to specificities of robotics problems in this context such as the use of non-Euclidean quantities, the necessity to handle singularities or the need for multiple levels of priority. In particular, taking advantage of the properties and structures induced allows to write very efficient dedicated solvers.
Going efficiently from the theoretical formulation of a motion optimization problem to its actual implementation and resolution on a real robot requires a large amount of coding and is error-prone. I will also briefly talk about frameworks and libraries I contributed to, targeting primarily whole-body control, that reduces that difficulty and present several demonstrations relying on them.
I will then finish with some perspectives related to my current and future researches.