Trajectory optimization

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 the 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, back flips, 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.