MIT Robotics - Jessy Grizzle - Mathematics and Learning for Bipedal Locomotion
Jessy Grizzle, distinguished professor of engineering and director of the Robotics Institute at the University of Michigan, discusses mathematics, learning, and feedback control for bipedal locomotion at an MIT Robotics seminar.
In this talk
- 10:14
Why use full robot models
Grizzle models walking as a hybrid system, with continuous motion during each step and an impact map when a foot lands. He argues that simplified pendulum models can miss practical constraints such as joint torque, power, and workspace limits. His group uses trajectory optimization to find periodic walking motions that respect those constraints.
- 13:54
From a walking motion to feedback
Grizzle describes virtual constraints that relate torso, knee, and hip motion to a spatial phase variable. Driving those constraints toward zero turns an optimized walking motion into a feedback controller. The method helped robots including RABBIT, MABEL, and MARLO walk, but MARLO’s controller struggled outdoors with stiction and uneven ground.
- 18:26
Learning to recover from disturbances
After early controllers failed outside the lab, Grizzle’s team added disturbed conditions to controller design so the robot could adjust and return toward its periodic motion. Dennis Da’s approach uses supervised machine learning to build a feedback policy from optimized trajectories. The goal is to select a feasible trajectory that passes through the robot’s current state, so the controller can respond immediately after a push.
- 43:35
Scaling the method to 3D terrain
MARLO has 16 dimensions in single support, making a dense trajectory library impractical; Grizzle estimates that five samples per dimension would require 152 billion optimizations. Da reduces the problem by separating a few weakly actuated states from the more strongly actuated ones, then building a surface of feasible trajectories. The resulting controller helped MARLO cross small humps in Michigan’s Wave Field, though the robot broke a leg on the larger humps.
- 55:24
What the method can and cannot guarantee
For different walking speeds, the team designs manifolds for multiple speeds and interpolates between them during a gait. Grizzle says the team cannot yet predict terrain robustness in advance or certify performance across specified terrain conditions. They use simulations and experience with each robot to focus robustness where its mechanics are weakest.
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