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Section: New Results
Robotics
Lexicographic Least-Squares solver
Participants : Pierre-Brice Wieber, Dimitar Dimitrov.
We have been working on Multi-Objective Least-Squares problems with inequality constraints for the last few years, focusing especially on the Lexicographic case. A previous collaboration with LAAS-CNRS and CEA-LIST led to the development of a software, SOTHÂ , based on Complete Orthogonal Decompositions, which has become a de facto reference in robotics when controlling robots (mobile, manipulator or humanoid) through constraints. The focus this year in the Bipop team has been to accelerate computations by reworking the inner matrix decomposition by combining QR and LU decompositions. The resulting solver, called LexLS, is approximately 5 times faster than the previous SOTH solver on most problems. But the main result has been to show both in theory and practice that it is faster to solve a Lexicographic problem than a Weighted problem, on the contrary to popular beliefs both in robotics and optimization theory. That leads to a reversal of popular approaches that prefer to solve weighted problems (thought to be faster to solve) as approximations to lexicographic problems (thought to be slower to solve).
Mobile manipulation by humanoid robots
Participants : Pierre-Brice Wieber, Dimitar Dimitrov, Alexander Sherikov, Jory Lafaye.
The realization of mobile manipulation by humanoid robots requires the handling of two simultaneous problems: taking care of the dynamic balance of the robot, what is usually done with Model Predictive Control (MPC) schemes, and redundant motion and force control of the whole body of the robot, what is usually done with a Quadratic Program, or a more advanced Lexicographic Least-Squares problem (see above). These two problems are usually solved in sequence: an MPC scheme first computes the necessary motion of the feet and Center of Mass (CoM) of the robot, then motion and force redundancy of the whole body of the robot is resolved. We have observed that this sequence corresponds to a lexicographic order between two objectives, feet and CoM motion first, the rest of the body after, which limits the possibility to tackle scenarios where we would like the motion of the CoM of the robot to be driven by the motion of the rest of the body of the robot, for example to catch an object with the hand. We have proposed therefore to reorganize the order between these different objectives, building on the LexLS solver presented above.
Reactive trajectory generation
Participants : Pierre-Brice Wieber, Dimitar Dimitrov, Saed Al Homsy, Matthieu Guilbert.
The goal of the ongoing collaboration with Adept Technologies is to generate near time optimal trajectories in the presence of moving obstacles in real time. Results are not public yet due to industrial constraints.