22 research outputs found
First Steps Towards Full Model Based Motion Planning and Control of Quadrupeds: A Hybrid Zero Dynamics Approach
The hybrid zero dynamics (HZD) approach has become a powerful tool for the gait planning and control of bipedal robots. This paper aims to extend the HZD methods to address walking, ambling and trotting behaviors on a quadrupedal robot. We present a framework that systematically generates a wide range of optimal trajectories and then provably stabilizes them for the full-order, nonlinear and hybrid dynamical models of quadrupedal locomotion. The gait planning is addressed through a scalable nonlinear programming using direct collocation and HZD. The controller synthesis for the exponential stability is then achieved through the Poincaré sections analysis. In particular, we employ an iterative optimization algorithm involving linear and bilinear matrix inequalities (LMIs and BMIs) to design HZD-based controllers that guarantee the exponential stability of the fixed points for the Poincaré return map. The power of the framework is demonstrated through gait generation and HZD-based controller synthesis for an advanced quadruped robot, —Vision 60, with 36 state variables and 12 control inputs. The numerical simulations as well as real world experiments confirm the validity of the proposed framework
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
Hierarchical and Safe Motion Control for Cooperative Locomotion of Robotic Guide Dogs and Humans: A Hybrid Systems Approach
This paper presents a hierarchical control strategy based on hybrid systems
theory, nonlinear control, and safety-critical systems to enable cooperative
locomotion of robotic guide dogs and visually impaired people. We address
high-dimensional and complex hybrid dynamical models that represent
collaborative locomotion. At the high level of the control scheme, local and
nonlinear baseline controllers, based on the virtual constraints approach, are
designed to induce exponentially stable dynamic gaits. The baseline controller
for the leash is assumed to be a nonlinear controller that keeps the human in a
safe distance from the dog while following it. At the lower level, a real-time
quadratic programming (QP) is solved for modifying the baseline controllers of
the robot as well as the leash to avoid obstacles. In particular, the QP
framework is set up based on control barrier functions (CBFs) to compute
optimal control inputs that guarantee safety while being close to the baseline
controllers. The stability of the complex periodic gaits is investigated
through the Poincare return map. To demonstrate the power of the analytical
foundation, the control algorithms are transferred into an extensive numerical
simulation of a complex model that represents cooperative locomotion of a
quadrupedal robot, referred to as Vision 60, and a human model. The complex
model has 16 continuous-time domains with 60 state variables and 20 control
inputs
Hybrid disturbance rejection control of dynamic bipedal robots
This paper presents a disturbance rejection control strategy for hybrid dynamic systems exposed to model uncertainties and external disturbances. The focus of this work is the gait control of dynamic bipedal robots. The proposed control strategy integrates continuous and discrete control actions. The continuous control action uses a novel model-based active disturbance rejection control (ADRC) approach to track gait trajectory references. The discrete control action resets the gait trajectory references after the impact produced by the robot’s support-leg exchange to maintain a zero tracking error. A Poincaré return map is used to search asymptotic stable periodic orbits in an extended hybrid zero dynamics (EHZD). The EHZD reflects a lower-dimensional representation of the full hybrid dynamics with uncertainties and disturbances. A physical bipedal robot testbed, referred to as Saurian, is fabricated for validation purposes. Numerical simulation and physical experiments show the robustness of the proposed control strategy against external disturbances and model uncertainties that affect both the swing motion phase and the support-leg exchange