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Trajectory Optimization (TO) and Model Predictive Control (MPC) are model-based optimization approaches, built upon Optimal Control theory, which are becoming increasingly popular in robotics. They offer an automatic way to synthesize and stabilize highly dynamic and contact-rich motions: a possibility which ...

Trajectory Optimization (TO) and Model Predictive Control (MPC) are model-based optimization approaches, built upon Optimal Control theory, which are becoming increasingly popular in robotics. They offer an automatic way to synthesize and stabilize highly dynamic and contact-rich motions: a possibility which is appealing to any robotic system but in particular to legged robots, as humanoids or quadrupeds.

While TO is commonly used to plan complex open-loop trajectories over a long prediction horizon, MPC enables fast replanning and feedback stabilization, over a shorter horizon.

Thanks to the combination of these techniques, legged systems are now able to seamlessly navigate through complex environments, jump, run, do back-flips and possibly much more in the years to come.

However, it remains an open question how to effectively employ TO and MPC on real legged systems. This requires smart formulations of the contact-constrained robot dynamics, convenient models of the environment, as well as computationally efficient and real-time optimizations algorithms.

The aim of this Research Topic is to inform the robotics research community of the newest findings and future directions in TO and MPC applied to legged systems.

This Research Topic will target contributions in the following areas involving humanoids, quadrupedal robots and dynamic legged systems in general:
• Real-hardware implementation of TO and MPC for dynamic tasks
• Whole-body loco-manipulation planning and control
• Automatic synthesis of highly dynamic and contact-rich motions
• New software tools for nonlinear optimal control
• Recent developments in optimization algorithms and real-time optimization
• Formulation of appropriate dynamical models for offline and online optimization
• Perception and modelling of complex environments for TO and MPC

Through a comprehensive selection of the newest ground-breaking contributions in this field, we hope to raise awareness and excitement around the opportunities offered by TO and MPC in legged robotics.


Dr. Enrico Mingo Hoffman will move to PAL Robotics as Senior Researcher in September 2021 while Dr. Matteo Parigi Polverini is with Agility Robotics as Robotics Controls/Planning Engineer from April 2021.

Keywords: Trajectory Optimization, Model Predictive Control, Humanoid Robots, Whole-Body Control, Legged Robots, Optimization


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