MIT研发 Whole-Body Impulse 控制与模型预测控制的高动态四足机器人行进

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"本文主要探讨了麻省理工学院（MIT）在高度动态四足机器人运动控制领域的创新工作，名为'Highly Dynamic Quadruped Locomotion via Whole-Body Impulse Control and Model Predictive Control'。研究团队由Donghyun Kim、Jared DiCarlo、Benjamin Katz、Gerardo Bledt和Sangbae Kim等人组成。动态腿部 locomotion 是一个极具挑战性的课题，因为现有的控制方案往往难以处理空中阶段、短步态时间和高速腿部摆动。在这个研究中，研究人员提出了一种结合了全身控制（Whole-Body Control, WBC）和模型预测控制（Model Predictive Control, MPC）的方法。核心思想是，MPC通过一个简单的模型，在较长的时间尺度上寻找最优的反应力分配。WBC则根据MPC计算出的反应力，进一步计算关节扭矩、位置和速度指令。这种设计与传统WBC方法不同，后者倾向于跟踪预设的身体轨迹，而新控制器更侧重于反应力命令的控制，从而实现高速且具有空中阶段的动态运动。为了验证控制器的鲁棒性和灵活性，实验在Mini-Cheetah四足机器人上进行了广泛的测试。实验覆盖了六种不同的步态，并在多种环境中进行，包括户外环境，旨在展示其在复杂动态条件下的性能。这种新型的WBC-MPC结合策略旨在提升四足机器人的运动性能，使之能够在各种动态挑战下稳定、高效地移动，这对于未来机器人技术，特别是适用于搜救、物流等领域有着重要的意义。"

Highly Dynamic Quadruped Locomotion via

Whole-Body Impulse Control and Model Predictive Control

Donghyun Kim

, Jared Di Carlo

, Benjamin Katz

, Gerardo Bledt

, and Sangbae Kim

Abstract— Dynamic legged locomotion is a challenging topic

because of the lack of established control schemes which can

handle aerial phases, short stance times, and high-speed leg

swings. In this paper, we propose a controller combining whole-

body control (WBC) and model predictive control (MPC). In

our framework, MPC ﬁnds an optimal reaction force proﬁle

over a longer time horizon with a simple model, and WBC

computes joint torque, position, and velocity commands based

on the reaction forces computed from MPC. Unlike existing

WBCs, which attempt to track commanded body trajectories,

our controller is focused more on the reaction force command,

which allows it to accomplish high speed dynamic locomotion

with aerial phases. The newly devised WBC is integrated

with MPC and tested on the Mini-Cheetah quadruped robot.

To demonstrate the robustness and versatility, the controller

is tested on six different gaits in a number of different

environments, including outdoors and on a treadmill, reaching

a top speed of 3.7 m/s.

I. INTRODUCTION

To fully exploit the hardware capability of legged systems,

we need a controller that can address the challenging issues

related to dynamic locomotion, such as body control during

short stance periods, aerial phases, and high speed swing leg

motion control. Several successful cases for both running

bipeds [1], [2] and quadrupeds [3] have been presented, but

they are either difﬁcult to scale up to high degree-of-freedom

systems [1] or heavily rely on speciﬁc system dynamics [2]

or are undocumented [3]. Whole-body control (WBC) is a

strong candidate as a dynamic motion controller because of

its dynamically consistent formulation and general frame-

work, which makes it easy to extend to various systems and

tasks. However, existing WBCs focus on how to follow the

given trajectory by manipulating contact forces, which makes

it nontrivial to address motion involving frequent non-contact

phases such as high speed running.

To tackle the issue, we formulate WBC to follow both

the reaction force and body trajectory commands. The idea

of reaction force tracking originates from the impulse plan-

ning used in Cheetah 2 [4], which demonstrates successful

dynamic bounding and jumping. The underlying idea of [4]

is to plan reaction forces, which are impulses, rather than

CoM trajectory, which is not practical to follow when the

locomotion is extremely dynamic and has signiﬁcant periods

of under-actuation. In this paper, we embrace the impulse

planning idea in WBC and formulate whole-body impulse

Authors are with the

Department of Mechanical Engineering at the

Massachusetts Institute of Technology, and the

Department of Elec-

trical Engineering and Computer Science at the Massachusetts Institute

of Technology, Cambridge, MA, 02139, USA. Corresponding Author:

robot.dhkim@gmail.com

Simplified model

Full body dynamics

Actual robot (Mini-Cheetah)

MPC (0.04kHz)

WBC (0.5kHz)

Fig. 1. Control Architecture. The proposed control architecture consists

of two parts: Model predictive control and whole-body control. The reaction

forces computed by MPC are modiﬁed by WBC to incorporate body

stabilization and swing leg control. The ﬁnal commands found in WBC

are sent to the robot to perform dynamic locomotion.

control (WBIC) that can incorporate both body posture stabi-

lization and reaction force execution. In terms of formulation,

WBIC is not signiﬁcantly different from the existing whole-

body controllers [5]–[7], but the additional feature, which is

an incorporation of pre-computed reaction forces by relaxing

the ﬂoating base control, plays an important role in dynamic

locomotion control. In our formulation, the WBIC is mostly

used to track the ground reaction force proﬁle rather than a

body trajectory.

To ﬁnd the reaction force command, we utilize model

predictive control (MPC). In our previous work, we demon-

strated that convex MPC can perform various dynamic gaits

at high speed on both Cheetah 3 [8] and Mini-Cheetah [9].

Utilization of MPC enhances the versatility of locomotion,

enabling us to switch between various gaits by simply

changing the contact sequence. However, using MPC with

a simple model has a fundamental limitation in position

control because of its low update frequency (40 Hz in our

implementations) and model simpliﬁcations. WBC provides

a solution to the MPC’s limitation by running a high-

frequency feedback loop while still accounting for full-body

dynamics with contact.

On the other hand, the prediction horizon of MPC com-

pliments the WBC perfectly to ﬁll in the WBC’s limita-

tion that it cannot consider more than a single time step

ahead. This limited time horizon issue has been addressed

in [10], [11] which developed an MPC formulation using

full-body dynamics. However, even their highly optimized

solvers barely ﬁt into a 200 Hz update frequency and the

arXiv:1909.06586v1 [cs.RO] 14 Sep 2019

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