Fast Trajectory Optimization for Legged Robots Using Vertex-Based ZMP Constraints
Alexander W. Winkler,Farbod Farshidian,Diego Pardo,Michael Neunert,Jonas Buchli +4 more
- Vol. 2, Iss: 4, pp 2201-2208
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TLDR
In this paper, a vertex-based representation of the support area constraint is introduced, which can treat arbitrarily oriented point-, line-, and area-contacts uniformly, allowing to generate diverse motions such as quadrupedal walking, trotting, bounding, pacing, combinations, and transitions between these.Abstract:
This letter combines the fast zero-moment-point approaches that work well in practice with the broader range of capabilities of a trajectory optimization formulation, by optimizing over body motion, footholds, and center of pressure simultaneously. We introduce a vertex-based representation of the support-area constraint, which can treat arbitrarily oriented point-, line-, and area-contacts uniformly. This generalization allows us to create motions, such as quadrupedal walking, trotting, bounding, pacing, combinations, and transitions between these, limping, bipedal walking, and push recovery all with the same approach. This formulation constitutes a minimal representation of the physical laws (unilateral contact forces) and kinematic restrictions (range of motion) in legged locomotion, which allows us to generate diverse motions in less than a second. We demonstrate the feasibility of the generated motions on a real quadruped robot.read more
Citations
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Journal ArticleDOI
Learning agile and dynamic motor skills for legged robots
Jemin Hwangbo,Joonho Lee,Alexey Dosovitskiy,Dario Bellicoso,Vassilios Tsounis,Vladlen Koltun,Marco Hutter +6 more
TL;DR: In this paper, a method for training a neural network policy in simulation and transferring it to a state-of-the-art legged system is presented. But this method is limited to simulation and only few and comparably simple examples have been deployed on real systems.
Proceedings ArticleDOI
Dynamic Locomotion in the MIT Cheetah 3 Through Convex Model-Predictive Control
TL;DR: This paper presents an implementation of model predictive control (MPC) to determine ground reaction forces for a torque-controlled quadruped robot, capable of robust locomotion at a variety of speeds.
Journal ArticleDOI
Gait and Trajectory Optimization for Legged Systems Through Phase-Based End-Effector Parameterization
TL;DR: A single trajectory optimization formulation for legged locomotion that automatically determines the gait sequence, step timings, footholds, swing-leg motions, and six-dimensional body motion over nonflat terrain, without any additional modules is presented.
Journal ArticleDOI
Learning agile and dynamic motor skills for legged robots
Jemin Hwangbo,Joonho Lee,Alexey Dosovitskiy,Dario Bellicoso,Vassilios Tsounis,Vladlen Koltun,Marco Hutter +6 more
TL;DR: This work introduces a method for training a neural network policy in simulation and transferring it to a state-of-the-art legged system, thereby leveraging fast, automated, and cost-effective data generation schemes.
Journal ArticleDOI
Dynamic Locomotion Through Online Nonlinear Motion Optimization for Quadrupedal Robots
TL;DR: This letter presents a realtime motion planning and control method that enables a quadrupedal robot to execute dynamic gaits including trot, pace, and dynamic lateral walk, as well as gaits with full flight phases such as jumping, pronking, and running trot.
References
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Biped walking pattern generation by using preview control of zero-moment point
Shuuji Kajita,Fumio Kanehiro,Kenji Kaneko,Kiyoshi Fujiwara,Kensuke Harada,Kazuhito Yokoi,Hirohisa Hirukawa +6 more
TL;DR: A new method of a biped walking pattern generation by using a preview control of the zero-moment point (ZMP) is introduced and a preview controller can be used to compensate the ZMP error caused by the difference between a simple model and the precise multibody model.
Journal ArticleDOI
Zero-moment point — thirty five years of its life
TL;DR: The paper gives an in-depth discussion of source results concerning ZMP, paying particular attention to some delicate issues that may lead to confusion if this method is applied in a mechanistic manner onto irregular cases of artificial gait, i.e. in the case of loss of dynamic balance of a humanoid robot.
Journal ArticleDOI
Direct trajectory optimization using nonlinear programming and collocation
C. R. Hargraves,Stephen W. Paris +1 more
TL;DR: In this article, an algorithm for the direct numerical solution of an optimal control problem is given, which employs cubic polynomials to represent state variables, linearly interpolates control variables, and uses collocation to satisfy the differential equations.