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详细说明：mit猎豹的不同四足步态预测控制算法，Policy regularized model Predictive Control Framework for
Robust Legged Locomotion
Gerardo bleat
Submitted to the department of mechanical Engineering
Department of Electrical Engineering and Computer Science
on December 15, 2017, in partial fulfillment of the
requirements for the degrees of
Master of Science in Mechanical Engineering
nd
Master of Science in Electrical Engineering and Computer Science
Abstract
A novel Policy Regularized Model Predictive Control(PR-MPC) framework is de-
veloped to allow general robust legged locomotion with the MIT Cheetah quadruped
robot. The full system is approximated by a simple control model that retains the key
nonlinearities characteristic to legged contact dynamics while reducing the complexity
of the continuous dynamics. Nominal footstep locations and feedforward forces for
controlling the robot's center of mass are designed from simple physics-based heuris-
tics for steady state legged movement. By regularizing the predictive optimization
with these policies, we can exploit the known dynamics of the system to bias the
ontroller towards the steady state gait while remaining free to explore the cost space
during transient behaviors and disturbances. The nonlinear optimization makes use
of direct collocation on the simplified dynamics to pose the problem with a highly
sparse structure for fast computation. a generalized approach to the controller design
is independent from specific gait pattern and reference policy and allows stabilization
of aperiodic locomotion. Simulation results show dynamic capabilities in a variety of
gaits including trotting, bounding, and galloping, all without changing the set of algo
rithm parameters between experiments. Robustness to sensor and input noise, large
push disturbances, and unstructured terrain demonstrate the ability of the predictive
controller to adapt to uncertainty
nesis
pervIsor
angbae Kim
Title: Associate Professor of Mechanical Engineering
Thesis supervisor: Russ Tedra ke
Title: Professor of Electrical Engineering and Computer Science
4
Acknowledgments
First, I want to share my appreciation for the love and encouragement from my
parents Carlos and Marcela throughout my whole life. Without them, none of what I
have accomplished would have been possible. I dedicate the work in this thesis to my
brother carlos who was immensely influential in my decision to follow in his footsteps
to become an engineer and pursue research at a higher level
I express my gratitude to my advisor Sangbae Kim for allowing me the opportunity
to work on a project that I am passionate about granting me the freedom to explore a
topic that i enjoy, and providing a wealth of intuition in the field of robotics. As part
of the Biomimetic Robotics Lab, I want to thank my labmates(including Cheetah)
for making my time in the lab and on the project fun and successful. In particular, a
huge thanks to Pat Wensing who helped guide me through the research process and
provided an endless amount of information that made this thesis a success. a thanks
to my thesis supervisor russ Tedrake for having accepted to work with me as part of
msrP before coming to Mif and then again for this thesis
Also, I would like to thank everyone who has helped me with all of the aspects of
graduate school other than research. Especially Leslie Regan and Janet Fischer for
all of their support throughout this year and being so accommodating to all of the
changes and difficulties during my time working towards completing the degrees. It
made the whole process much simpler which has been very appreciated
Lastly, thanks to all my friends throughout my life in Madison, Virginia Tech, and
MIT that have made my time outside of the lab and academics enjoyable and filled
with great memories. They have provided a much needed distraction from all of the
work associated with research
6
Contents
1 Introduction
15
1.1 Impacts of Mobile robots
15
1.1.1 Advances and challenges in legged robotics
17
1.2 Predictive Control
19
1.3 Contribution
20
2 Theory and System Modeling
23
2.1 Robot model
23
2.1.1 Kinematics
23
2.1.2 dynamics
24
2.2 Gait Scheduling
28
3 Predictive Control formulation
31
3.1 Simplified Discrete Dynamics
3.2 Generalized prediction horizon
3.3 Physics-Based Policy regularizer
36
3.4 PR-MPC Formulation
38
3.4.1 Cost Function
3.4.2 Constraints
40
4 Simulation results
45
4.1 From Naive mPc to PR-MPc
4.2 Basic locomotion
48
4.3 Robustness Testing
4.3.1 Disturbance rejection environment Uncertainty
22
5
4.3.2 Diverse Gait Stabilization
55
4.4 Computation Timings
57
5 Conclusion
61
3.1 Future Work
61
5.1.1 Implementation on the MIT Cheetah 3 Robot
62
5.1.2 Algorithm Improvements
64
5.2 Implications
List of figures
1-1 MIT Cheetah 2 Robot. Experimental legged robotic platform de
veloped by the Biomimetic Robotics Lab at Mit
19
1-2 Capabilities of PR-MPC. The novel framework allows for a wide
variety of dynamic capabilities across multiple gaits and under distur-
bances with uncertain environments
21
2-1 Kinematic Tree Model. The robot's kinematics are defined as a
kinematic tree composed of kinematic chains attached to a free floating
base
24
2-2 Physical System Definitions. Coordinate systems and definitions
for the rigid body model in 3D. The vectors r, specify the position of
each foot relative to the body Com, while forces f, provide the force
Inder each foot
2-3 Trot Gait Pattern. A gait pattern map for the running trot that
defines contact states for the leg over time with a red bar and swing
phases otherwise. Distinct contact phases are notted by the dashed
black lines
28
3-1 Autonomous Navigation Plan. The robot will receive a goal state
and autonomously generate a locomotion plan to safely navigate its
environment
3-2 Overall System Framework. Proposed block diagram framework
for autonomous navigation with the IT Cheetah. Detailed descrip-
tions of the white blocks are presented while gray blocks represent
components that are outside the scope of this work
32
3-3 Gaited Prediction Horizon Definition. An example prediction
horizon definition for the running trot gait with Gait=N=4,K
9. The algorithm returns an optimized plan for all n phases depicted
in blue, but executes only the first planned phase outlined in green.. 36
3-4 Physical Constraint Depiction. The optimization is constrained
to remain physically feasible throughout the prediction horizon
40
4-1 Case A: Naive MPC. Without any information from the simple
physics references, the optimization returns forces and foot placements
at local minima that is unable to stabilize the robot even during standing. 46
4-2 Case B: Force Seeded MPC. Resultant footstep locations without
any footstep placement seeding or regularization cluster under the CoM. 47
4-3 Case C: Fully Seeded MPC. Resultant footstep locations with a
given footstep placement seeding, but no regularization........ 47
4-4 Case D: PR-MPC. Resultant footstep locations with both a seeded
initial footstep location reference, as well as regularization for the full
PR-MPC case
48
4-5 Predicted Footstep Planning. A receding prediction horizon for
planning returns N future footstep locations for each foot. The next
predicted footstep is used for planning the swing foot trajectories
49
4-6 Accelerating From Rest. From rest, the controller is able to ac-
celerate to a nominal steady state trotting pace while stabilizing the
transient behavior during the acceleration periods
50
4-7 Rapid Yawing. The robot turns with a commanded 30 1 and rolls
to match the natural motion expected from the conical pendulum model. 51
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