72 research outputs found
Cooperative Adaptive Control for Cloud-Based Robotics
This paper studies collaboration through the cloud in the context of
cooperative adaptive control for robot manipulators. We first consider the case
of multiple robots manipulating a common object through synchronous centralized
update laws to identify unknown inertial parameters. Through this development,
we introduce a notion of Collective Sufficient Richness, wherein parameter
convergence can be enabled through teamwork in the group. The introduction of
this property and the analysis of stable adaptive controllers that benefit from
it constitute the main new contributions of this work. Building on this
original example, we then consider decentralized update laws, time-varying
network topologies, and the influence of communication delays on this process.
Perhaps surprisingly, these nonidealized networked conditions inherit the same
benefits of convergence being determined through collective effects for the
group. Simple simulations of a planar manipulator identifying an unknown load
are provided to illustrate the central idea and benefits of Collective
Sufficient Richness.Comment: ICRA 201
Numerical Methods to Compute the Coriolis Matrix and Christoffel Symbols for Rigid-Body Systems
The growth of model-based control strategies for robotics platforms has led
to the need for additional rigid-body-dynamics algorithms to support their
operation. Toward addressing this need, this article summarizes efficient
numerical methods to compute the Coriolis matrix and underlying Christoffel
Symbols (of the first kind) for tree-structure rigid-body systems. The
resulting algorithms can be executed purely numerically, without requiring any
partial derivatives that would be required in symbolic techniques that do not
scale. Properties of the presented algorithms share recursive structure in
common with classical methods such as the Composite-Rigid-Body Algorithm. The
algorithms presented are of the lowest possible order: for the Coriolis
Matrix and for the Christoffel symbols, where is the number of
bodies and is the depth of the kinematic tree. A method of order is
also provided to compute the time derivative of the mass matrix. A numerical
implementation of these algorithms in C/C++ is benchmarked showing computation
times on the order of 10-20 s for the computation of the Coriolis matrix
and s for the computation of the Christoffel symbols for systems
with degrees of freedom. These results demonstrate feasibility for the
adoption of these numerical methods within control loops that need to operate
at kHz rates or higher, as is commonly required for model-based control
applications
Tensor-Free Second-Order Differential Dynamic Programming
This paper presents a method to reduce the computational complexity of
including second-order dynamics sensitivity information into the Differential
Dynamic Programming (DDP) trajectory optimization algorithm. A tensor-free
approach to DDP is developed where all the necessary derivatives are computed
with the same complexity as in the iterative Linear Quadratic Regulator~(iLQR).
Compared to linearized models used in iLQR, DDP more accurately represents the
dynamics locally, but it is not often used since the second-order derivatives
of the dynamics are tensorial and expensive to compute. This work shows how to
avoid the need for computing the derivative tensor by instead leveraging
reverse-mode accumulation of derivative information to compute a key
vector-tensor product directly. We benchmark this approach for trajectory
optimization with multi-link manipulators and show that the benefits of DDP can
often be included without sacrificing evaluation time, and can be done in fewer
iterations than iLQR
Online Planning for Autonomous Running Jumps Over Obstacles in High-Speed Quadrupeds
This paper presents a new framework for the generation of high-speed running jumps to clear terrain obstacles in quadrupedal robots. Our methods enable the quadruped to autonomously jump over obstacles up to 40 cm in height within a single control framework. Specifically, we propose new control system components, layered on top of a low-level running controller, which actively modify the approach and select stance force profiles as required to clear a sensed obstacle. The approach controller enables the quadruped to end in a preferable state relative to the obstacle just before the jump. This multi-step gait planning is formulated as a multiple-horizon model predictive control problem and solved at each step through quadratic programming. Ground reaction force profiles to execute the running jump are selected through constrained nonlinear optimization on a simplified model of the robot that possesses polynomial dynamics. Exploiting the simplified structure of these dynamics, the presented method greatly accelerates the computation of otherwise costly function and constraint evaluations that are required during optimization. With these considerations, the new algorithms allow for online planning that is critical for reliable response to unexpected situations. Experimental results, for a stand-alone quadruped with on-board power and computation, show the viability of this approach, and represent important steps towards broader dynamic maneuverability in experimental machines.United States. Defense Advanced Research Projects Agency. Maximum Mobility and Manipulation (M3) ProgramKorean Agency for Defense Development (Contract UD1400731D
Multi-Shooting Differential Dynamic Programming for Hybrid Systems using Analytical Derivatives
Differential Dynamic Programming (DDP) is a popular technique used to
generate motion for dynamic-legged robots in the recent past. However, in most
cases, only the first-order partial derivatives of the underlying dynamics are
used, resulting in the iLQR approach. Neglecting the second-order terms often
slows down the convergence rate compared to full DDP. Multi-Shooting is another
popular technique to improve robustness, especially if the dynamics are highly
non-linear. In this work, we consider Multi-Shooting DDP for trajectory
optimization of a bounding gait for a simplified quadruped model. As the main
contribution, we develop Second-Order analytical partial derivatives of the
rigid-body contact dynamics, extending our previous results for fixed/floating
base models with multi-DoF joints. Finally, we show the benefits of a novel
Quasi-Newton method for approximating second-order derivatives of the dynamics,
leading to order-of-magnitude speedups in the convergence compared to the full
DDP method.Comment: https://www.youtube.com/watch?v=C0h6mEpcnA
A Unified Perspective on Multiple Shooting In Differential Dynamic Programming
Differential Dynamic Programming (DDP) is an efficient computational tool for
solving nonlinear optimal control problems. It was originally designed as a
single shooting method and thus is sensitive to the initial guess supplied.
This work considers the extension of DDP to multiple shooting (MS), improving
its robustness to initial guesses. A novel derivation is proposed that accounts
for the defect between shooting segments during the DDP backward pass, while
still maintaining quadratic convergence locally. The derivation enables
unifying multiple previous MS algorithms, and opens the door to many smaller
algorithmic improvements. A penalty method is introduced to strategically
control the step size, further improving the convergence performance. An
adaptive merit function and a more reliable acceptance condition are employed
for globalization. The effects of these improvements are benchmarked for
trajectory optimization with a quadrotor, an acrobot, and a manipulator. MS-DDP
is also demonstrated for use in Model Predictive Control (MPC) for dynamic
jumping with a quadruped robot, showing its benefits over a single shooting
approach
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