589 research outputs found
Asymptotically Stable Walking of a Five-Link Underactuated 3D Bipedal Robot
This paper presents three feedback controllers that achieve an asymptotically
stable, periodic, and fast walking gait for a 3D (spatial) bipedal robot
consisting of a torso, two legs, and passive (unactuated) point feet. The
contact between the robot and the walking surface is assumed to inhibit yaw
rotation. The studied robot has 8 DOF in the single support phase and 6
actuators. The interest of studying robots with point feet is that the robot's
natural dynamics must be explicitly taken into account to achieve balance while
walking. We use an extension of the method of virtual constraints and hybrid
zero dynamics, in order to simultaneously compute a periodic orbit and an
autonomous feedback controller that realizes the orbit. This method allows the
computations to be carried out on a 2-DOF subsystem of the 8-DOF robot model.
The stability of the walking gait under closed-loop control is evaluated with
the linearization of the restricted Poincar\'e map of the hybrid zero dynamics.
Three strategies are explored. The first strategy consists of imposing a
stability condition during the search of a periodic gait by optimization. The
second strategy uses an event-based controller. In the third approach, the
effect of output selection is discussed and a pertinent choice of outputs is
proposed, leading to stabilization without the use of a supplemental
event-based controller
Imprecise dynamic walking with time-projection control
We present a new walking foot-placement controller based on 3LP, a 3D model
of bipedal walking that is composed of three pendulums to simulate falling,
swing and torso dynamics. Taking advantage of linear equations and closed-form
solutions of the 3LP model, our proposed controller projects intermediate
states of the biped back to the beginning of the phase for which a discrete LQR
controller is designed. After the projection, a proper control policy is
generated by this LQR controller and used at the intermediate time. This
control paradigm reacts to disturbances immediately and includes rules to
account for swing dynamics and leg-retraction. We apply it to a simulated Atlas
robot in position-control, always commanded to perform in-place walking. The
stance hip joint in our robot keeps the torso upright to let the robot
naturally fall, and the swing hip joint tracks the desired footstep location.
Combined with simple Center of Pressure (CoP) damping rules in the low-level
controller, our foot-placement enables the robot to recover from strong pushes
and produce periodic walking gaits when subject to persistent sources of
disturbance, externally or internally. These gaits are imprecise, i.e.,
emergent from asymmetry sources rather than precisely imposing a desired
velocity to the robot. Also in extreme conditions, restricting linearity
assumptions of the 3LP model are often violated, but the system remains robust
in our simulations. An extensive analysis of closed-loop eigenvalues, viable
regions and sensitivity to push timings further demonstrate the strengths of
our simple controller
An Inverse Dynamics Approach to Control Lyapunov Functions
With the goal of moving towards implementation of increasingly dynamic behaviors on underactuated systems, this paper presents an optimization-based approach for solving full-body dynamics based controllers on underactuated bipedal robots. The primary focus of this paper is on the development of an alternative approach to the implementation of controllers utilizing control Lyapunov function based quadratic programs. This approach utilizes many of the desirable aspects from successful inverse dynamics based controllers in the literature, while also incorporating a variant of control Lyapunov functions that renders better convergence in the context of tracking outputs. The principal benefits of this formulation include a greater ability to add costs which regulate the resulting behavior of the robot. In addition, the model error-prone inertia matrix is used only once, in a non-inverted form. The result is a successful demonstration of the controller for walking in simulation, and applied on hardware in real-time for dynamic crouching
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
Impact-Aware Online Motion Planning for Fully-Actuated Bipedal Robot Walking
The ability to track a general walking path with specific timing is crucial
to the operational safety and reliability of bipedal robots for avoiding
dynamic obstacles, such as pedestrians, in complex environments. This paper
introduces an online, full-body motion planner that generates the desired
impact-aware motion for fully-actuated bipedal robotic walking. The main
novelty of the proposed planner lies in its capability of producing desired
motions in real-time that respect the discrete impact dynamics and the desired
impact timing. To derive the proposed planner, a full-order hybrid dynamic
model of fully-actuated bipedal robotic walking is presented, including both
continuous dynamics and discrete lading impacts. Next, the proposed
impact-aware online motion planner is introduced. Finally, simulation results
of a 3-D bipedal robot are provided to confirm the effectiveness of the
proposed online impact-aware planner. The online planner is capable of
generating full-body motion of one walking step within 0.6 second, which is
shorter than a typical bipedal walking step
Simultaneous optimization of gait and design parameters for bipedal robots
A walking bipedal robot’s energy efficiency depends on its gait as well as its design, whereas design changes affect the optimal gaits. We propose a method to take these interdependencies into account via simultaneous optimization of gait as well as design parameters. The method is applied to a planar robot with hybrid zero dynamics control and a torsion spring between its thighs. Periodic gaits are simulated by means of the hybrid zero dynamics. The implementation of the simultaneous optimization of gait parameters and spring stiffness via sequential quadratic programming is presented. Subsequently, an error analysis is performed to gain good convergence and short computation times of the optimization. The evaluation of gradients is identified as crucial for the algorithm’s convergence and therefore performed via complex step derivative approximations. The resulting implementation exhibits good convergence behavior and is provided as supplement to this paper. At 2.3 m/s, the simultaneous optimization results in savings in energy expenditure of up to 55%. A consecutive optimization of first gait and then stiffness yields only 11%, demonstrating the advantage of the presented method
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