The Biomimetic Robotics Lab at the Massachusetts Institute of Technology (MIT) has been using Artelys Knitro for real-time control of their legged robots: the MIT Mini Cheetah and the MIT Humanoid. Trajectory optimization is an essential process for real-time control of legged robots. Optimal control for legged systems is a challenging problem that must contend with nonlinear, hybrid dynamics and complicated, high degree-of-freedom kinematics. In the case of the Mini Cheetah, this optimization process is used to plan complicated motions such as jumps, aerial spins, backflips, and barrel rolls.
The ability to perform these motions greatly expands the range of environments the robot is capable of traversing, which is crucial as these robots are meant to be deployed operationally. Since incorporating Artelys Knitro into the software, the lab has been able to implement a number of new, real-time controllers on their robots using nonlinear optimization. Even after testing other state-of-the-art nonlinear optimization solvers, Artelys Knitro was the only one capable of performing fast enough to be deployed onboard their robot.
Model predictive controllers
For the Mini Cheetah, a nonlinear model predictive controller (MPC) was implemented for landing. The optimization was formulated with complementarity constraints, which make the nonlinear program (NLP) challenging for many solvers, but Artelys Knitro was able to find solutions at roughly 5-10 Hz (i.e., between 5 and 10 problems are solved every second). The team used a nonlinear trajectory optimization including contact complementary constraints to find optimal landing postures. Because real-time performance is so important in the short duration of a fall, Artelys Knitro was used over other solvers for its speed and reliable convergence.
For the MIT Humanoid, a nonlinear predictive controller was implemented that leverages the MIT Humanoid’s arms to improve balance and locomotion. The complex nonlinear optimization can solve complex arm motions in response to large disturbances. Artelys Knitro solved these motions at 40 Hz and helped demonstrate successful landings in both simulation and hardware.
If you want to know more about Artelys Knitro applications, you can contact us or visit the dedicated web page.
— Join Artelys on May 18th to learn more about Artelys Knitro, the most advanced solver for nonlinear optimization and ways to unleash the full potential of mathematical optimization.
— Artelys is thrilled to invite you to the METIS 2 Dissemination Event on May 31th. During this online event, we will present the METIS project’s latest results and discuss the benefits of using this modeling tool for energy and climate policymaking.
— As part of the METIS project, Artelys delivered a first model in 2018 to the European Commission. This year, Artelys has provided a major upgrade of the energy system model METIS.
Release of ADEME’s report “Modeling and optimizing French and European power mixes from 2020 to 2060”
— ADEME, the French energy and environment agency, contracted with Artelys to analyze four power systems scenarios.
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