Real-time Optimal Landing Control of the MIT Mini Cheetah

Authors: Se Hwan Jeon, Sangbae Kim, Donghyun Kim · ICRA 2022

Licences

Open Access
Paper: CC BY 4.0

Everything below draws on the full paper under its CC BY 4.0 licence; its figure is credited to the authors.

TL;DR

A landing controller re-solves a contact-implicit trajectory optimisation while the quadruped falls, warm-started by a neural network, then tracks it with whole-body control at touchdown.

Why it matters

Legged robots sent into rough or unsupervised terrain need to survive planned drops and unexpected falls without damage. The paper shows a contact-implicit optimisation can be made fast enough to choose landing contacts on the fly from different orientations and velocities.

Problem

Impedance control can stabilise a quadruped after small drops but fails at higher velocities or with large body tilt, and it does not choose landing posture, contact locations or contact order. Trajectory optimisation methods that optimise contact timing exist but have been too slow to run in real time.

Proposed solution

While airborne, the robot repeatedly solves a nonlinear trajectory optimisation on a single rigid body model with no-slip contact complementarity constraints, so contact order and timing come out of the solve rather than a fixed schedule. Joint velocities are dropped as decision variables, only the terminal state is penalised, foot box limits scale with body velocity, and a small neural network supplies the warm start. At touchdown, detected from joint-encoder velocities, a 500 Hz QP whole-body controller tracks the latest solution.

Key insights

Restricting contact complementarity constraints to no-slip contact gives more consistent and faster convergence than the full Coulomb sliding model
Penalising only the terminal state improved solve speed and sometimes solution quality; running costs on forces or states produced trajectories with knees penetrating the ground or forces before touchdown
Setting the initial height so touchdown is always expected after the first timestep makes the controller independent of the robot's global height above the ground
Foot touchdown angle correlated with centre-of-mass velocity direction, so velocity-scaled kinematic box limits were added to aid convergence
Recovery is far more sensitive to roll and lateral velocity than to pitch and forward velocity, since only one ab/ad motor per leg counters roll

Main results

Recovered from a horizontal drop of 8 m in simulation, corresponding to vertical velocity of roughly -12 m/s
In simulation, recovered from angular velocities of -0.5 to 0.5 rad/s, horizontal velocities of -1.5 to 1.5 m/s, pitch of -π/3 to π/3 and roll of -π/6 to π/6
Hardware landings from horizontal drops of up to 2 m with the robot released by hand
Neural-network warm start gave roughly 5-10× speedups in solve time over cold-start and two-stage warm-start optimisation
Solve rate is given as approximately 10 Hz in the introduction and as 5-8 Hz with MATLAB overhead in the real-time performance results
Warm-start network trained on roughly 1500 optimised trajectories; in simulation the high tracking error at impact goes to zero within the first 0.1 s

Limitations

Airborne state estimation drifted severely, so on hardware the falling conditions were hard coded rather than measured
Drops with significant pitch, roll or lateral velocity were not tested on hardware to avoid damaging the robot
Impact forces and instantaneous velocity changes at touchdown are ignored, and the authors say high-speed impacts need further study
Robustness to errors in the falling conditions and performance on uneven terrain are not yet characterised
The authors state that processor and power-board upgrades are needed to solve the problem fully untethered and onboard

Field impact

Finalist for the ICRA 2022 Outstanding Dynamics and Control Paper award, with 8 citations. The paper does not state a code or data release.

Abstract

Quadrupedal landing is a complex process involving large impacts, elaborate contact transitions, and is a crucial recovery behavior observed in many biological animals. This work presents a real-time, optimal landing controller that is free of pre-specified contact schedules. The controller determines optimal touchdown postures and reaction force profiles and is able to recover from a variety of falling configurations. The quadrupedal platform used, the MIT Mini Cheetah, recovered safely from drops of up to 8 m in simulation, as well as from a range of orientations and planar velocities. The controller is also tested on hardware, successfully recovering from drops of up to 2 m.

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