Leveraging Precision in Numerical Optimization for Robotic Motions

Automated vehicles and complex robot workers are expected to be used massively soon, with positive impacts on security, health at work and productivity.

To handle real-world situations, they need to compute their command as fast as possible, but the advanced, safe control algorithms remain a computational bottleneck.

To find the solution to a set of motion specifications and constraints for a robot, a widely used approach is to formulate and solve an optimization problem.

The formulation is necessarily imprecise, due to modeling, sensing and estimation errors and the solution will not be executed perfectly by the robot.

Yet the optimization solvers used in robotics are designed to converge to an exact solution with high precision, wasting time.In this project, I make a change of paradigm by leveraging approximations and investigate how the absence of need for high precision can be used to develop faster solvers.

I study what approximations or errors are acceptable for the problem formulation and the solution, paying attention to the numeric properties of the problem.

I use this knowledge to develop a solver tailored for approximate computations, with an emphasize on cheap but imprecise inner iterations and early termination.

It will also handle gracefully infeasible situations due to errors, making it safer to operate in real conditions.To make the study, and test and benchmark the solver, I focus on two families of control problems: model predictive control and instantaneous linearized control, applied to a wide variety of systems, from buses, to rockets, to humanoid robots.This solver will have important impacts: make it possible to achieve real-time control for the most complex system; allow to keep real-time, when it was already possible, while enriching the problems; reduce the computing power and energy consumption required for a given robot.

Understanding and handling imprecisions would also allow to build less precise and thus cheaper robots.