64 research outputs found
Dynamic Walking: Toward Agile and Efficient Bipedal Robots
Dynamic walking on bipedal robots has evolved from an idea in science fiction to a practical reality. This is due to continued progress in three key areas: a mathematical understanding of locomotion, the computational ability to encode this mathematics through optimization, and the hardware capable of realizing this understanding in practice. In this context, this review article outlines the end-to-end process of methods which have proven effective in the literature for achieving dynamic walking on bipedal robots. We begin by introducing mathematical models of locomotion, from reduced order models that capture essential walking behaviors to hybrid dynamical systems that encode the full order continuous dynamics along with discrete footstrike dynamics. These models form the basis for gait generation via (nonlinear) optimization problems. Finally, models and their generated gaits merge in the context of real-time control, wherein walking behaviors are translated to hardware. The concepts presented are illustrated throughout in simulation, and experimental instantiation on multiple walking platforms are highlighted to demonstrate the ability to realize dynamic walking on bipedal robots that is agile and efficient
Bipedal Hopping: Reduced-order Model Embedding via Optimization-based Control
This paper presents the design and validation of controlling hopping on the
3D bipedal robot Cassie. A spring-mass model is identified from the kinematics
and compliance of the robot. The spring stiffness and damping are encapsulated
by the leg length, thus actuating the leg length can create and control hopping
behaviors. Trajectory optimization via direct collocation is performed on the
spring-mass model to plan jumping and landing motions. The leg length
trajectories are utilized as desired outputs to synthesize a control Lyapunov
function based quadratic program (CLF-QP). Centroidal angular momentum, taking
as an addition output in the CLF-QP, is also stabilized in the jumping phase to
prevent whole body rotation in the underactuated flight phase. The solution to
the CLF-QP is a nonlinear feedback control law that achieves dynamic jumping
behaviors on bipedal robots with compliance. The framework presented in this
paper is verified experimentally on the bipedal robot Cassie.Comment: 8 pages, 7 figures, accepted by IROS 201
Virtual Constraints and Hybrid Zero Dynamics for Realizing Underactuated Bipedal Locomotion
Underactuation is ubiquitous in human locomotion and should be ubiquitous in
bipedal robotic locomotion as well. This chapter presents a coherent theory for
the design of feedback controllers that achieve stable walking gaits in
underactuated bipedal robots. Two fundamental tools are introduced, virtual
constraints and hybrid zero dynamics. Virtual constraints are relations on the
state variables of a mechanical model that are imposed through a time-invariant
feedback controller. One of their roles is to synchronize the robot's joints to
an internal gait phasing variable. A second role is to induce a low dimensional
system, the zero dynamics, that captures the underactuated aspects of a robot's
model, without any approximations. To enhance intuition, the relation between
physical constraints and virtual constraints is first established. From here,
the hybrid zero dynamics of an underactuated bipedal model is developed, and
its fundamental role in the design of asymptotically stable walking motions is
established. The chapter includes numerous references to robots on which the
highlighted techniques have been implemented.Comment: 17 pages, 4 figures, bookchapte
Trajectory Optimization and Machine Learning to Design Feedback Controllers for Bipedal Robots with Provable Stability
This thesis combines recent advances in trajectory optimization of hybrid dynamical systems with machine learning and geometric control theory to achieve unprecedented performance in bipedal robot locomotion. The work greatly expands the class of robot models for which feedback controllers can be designed with provable stability. The methods are widely applicable beyond bipedal robots, including exoskeletons, and prostheses, and eventually, drones, ADAS, and other highly automated machines.
One main idea of this thesis is to greatly expand the use of multiple trajectories in the design of a stabilizing controller. The computation of many trajectories is now feasible due to new optimization tools. The computations are not fast enough to apply in the real-time, however, so they are not feasible for model predictive control (MPC). The offline “library” approach will encounter the curse of dimensionality for the high-dimensional models common in bipedal robots. To overcome these obstructions, we embed a stable walking motion in an attractive low-dimensional surface of the system's state space. The periodic orbit is now an attractor of the low-dimensional state-variable model but is not attractive in the full-order system. We then use the special structure of mechanical models associated with bipedal robots to embed the low-dimensional model in the original model in such a manner that the desired walking motions are locally exponentially stable.
The ultimate solution in this thesis will generate model-based feedback controllers for bipedal robots, in such a way that the closed-loop system has a large stability basin, exhibits highly agile, dynamic behavior, and can deal with significant perturbations coming from the environment. In the case of bipeds: “model-based” means that the controller will be designed on the basis of the full floating-base dynamic model of the robot, and not a simplified model, such as the LIP (Linear Inverted Pendulum). By “agile and dynamic” is meant that the robot moves at the speed of a normal human or faster while walking off a curb. By “significant perturbation” is meant a human tripping, and while falling, throwing his/her full weight into the back of the robot.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145992/1/xda_1.pd
Beyond Basins of Attraction: Quantifying Robustness of Natural Dynamics
Properly designing a system to exhibit favorable natural dynamics can greatly
simplify designing or learning the control policy. However, it is still unclear
what constitutes favorable natural dynamics and how to quantify its effect.
Most studies of simple walking and running models have focused on the basins of
attraction of passive limit-cycles and the notion of self-stability. We instead
emphasize the importance of stepping beyond basins of attraction. We show an
approach based on viability theory to quantify robust sets in state-action
space. These sets are valid for the family of all robust control policies,
which allows us to quantify the robustness inherent to the natural dynamics
before designing the control policy or specifying a control objective. We
illustrate our formulation using spring-mass models, simple low dimensional
models of running systems. We then show an example application by optimizing
robustness of a simulated planar monoped, using a gradient-free optimization
scheme. Both case studies result in a nonlinear effective stiffness providing
more robustness.Comment: 15 pages. This work has been accepted to IEEE Transactions on
Robotics (2019
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