5,062 research outputs found
Sequential Convex Programming Methods for Solving Nonlinear Optimization Problems with DC constraints
This paper investigates the relation between sequential convex programming
(SCP) as, e.g., defined in [24] and DC (difference of two convex functions)
programming. We first present an SCP algorithm for solving nonlinear
optimization problems with DC constraints and prove its convergence. Then we
combine the proposed algorithm with a relaxation technique to handle
inconsistent linearizations. Numerical tests are performed to investigate the
behaviour of the class of algorithms.Comment: 18 pages, 1 figur
Adjoint-based predictor-corrector sequential convex programming for parametric nonlinear optimization
This paper proposes an algorithmic framework for solving parametric
optimization problems which we call adjoint-based predictor-corrector
sequential convex programming. After presenting the algorithm, we prove a
contraction estimate that guarantees the tracking performance of the algorithm.
Two variants of this algorithm are investigated. The first one can be used to
solve nonlinear programming problems while the second variant is aimed to treat
online parametric nonlinear programming problems. The local convergence of
these variants is proved. An application to a large-scale benchmark problem
that originates from nonlinear model predictive control of a hydro power plant
is implemented to examine the performance of the algorithms.Comment: This manuscript consists of 25 pages and 7 figure
A Method to Guarantee Local Convergence for Sequential Quadratic Programming with Poor Hessian Approximation
Sequential Quadratic Programming (SQP) is a powerful class of algorithms for
solving nonlinear optimization problems. Local convergence of SQP algorithms is
guaranteed when the Hessian approximation used in each Quadratic Programming
subproblem is close to the true Hessian. However, a good Hessian approximation
can be expensive to compute. Low cost Hessian approximations only guarantee
local convergence under some assumptions, which are not always satisfied in
practice. To address this problem, this paper proposes a simple method to
guarantee local convergence for SQP with poor Hessian approximation. The
effectiveness of the proposed algorithm is demonstrated in a numerical example
Contact-Implicit Trajectory Optimization Based on a Variable Smooth Contact Model and Successive Convexification
In this paper, we propose a contact-implicit trajectory optimization (CITO)
method based on a variable smooth contact model (VSCM) and successive
convexification (SCvx). The VSCM facilitates the convergence of gradient-based
optimization without compromising physical fidelity. On the other hand, the
proposed SCvx-based approach combines the advantages of direct and shooting
methods for CITO. For evaluations, we consider non-prehensile manipulation
tasks. The proposed method is compared to a version based on iterative linear
quadratic regulator (iLQR) on a planar example. The results demonstrate that
both methods can find physically-consistent motions that complete the tasks
without a meaningful initial guess owing to the VSCM. The proposed SCvx-based
method outperforms the iLQR-based method in terms of convergence, computation
time, and the quality of motions found. Finally, the proposed SCvx-based method
is tested on a standard robot platform and shown to perform efficiently for a
real-world application.Comment: Accepted for publication in ICRA 201
Real-Time Motion Planning of Legged Robots: A Model Predictive Control Approach
We introduce a real-time, constrained, nonlinear Model Predictive Control for
the motion planning of legged robots. The proposed approach uses a constrained
optimal control algorithm known as SLQ. We improve the efficiency of this
algorithm by introducing a multi-processing scheme for estimating value
function in its backward pass. This pass has been often calculated as a single
process. This parallel SLQ algorithm can optimize longer time horizons without
proportional increase in its computation time. Thus, our MPC algorithm can
generate optimized trajectories for the next few phases of the motion within
only a few milliseconds. This outperforms the state of the art by at least one
order of magnitude. The performance of the approach is validated on a quadruped
robot for generating dynamic gaits such as trotting.Comment: 8 page
A Family of Iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control
This paper introduces a family of iterative algorithms for unconstrained
nonlinear optimal control. We generalize the well-known iLQR algorithm to
different multiple-shooting variants, combining advantages like
straight-forward initialization and a closed-loop forward integration. All
algorithms have similar computational complexity, i.e. linear complexity in the
time horizon, and can be derived in the same computational framework. We
compare the full-step variants of our algorithms and present several simulation
examples, including a high-dimensional underactuated robot subject to contact
switches. Simulation results show that our multiple-shooting algorithms can
achieve faster convergence, better local contraction rates and much shorter
runtimes than classical iLQR, which makes them a superior choice for nonlinear
model predictive control applications.Comment: 8 page
A Simple and Efficient Algorithm for Nonlinear Model Predictive Control
We present PANOC, a new algorithm for solving optimal control problems
arising in nonlinear model predictive control (NMPC). A usual approach to this
type of problems is sequential quadratic programming (SQP), which requires the
solution of a quadratic program at every iteration and, consequently, inner
iterative procedures. As a result, when the problem is ill-conditioned or the
prediction horizon is large, each outer iteration becomes computationally very
expensive. We propose a line-search algorithm that combines forward-backward
iterations (FB) and Newton-type steps over the recently introduced
forward-backward envelope (FBE), a continuous, real-valued, exact merit
function for the original problem. The curvature information of Newton-type
methods enables asymptotic superlinear rates under mild assumptions at the
limit point, and the proposed algorithm is based on very simple operations:
access to first-order information of the cost and dynamics and low-cost direct
linear algebra. No inner iterative procedure nor Hessian evaluation is
required, making our approach computationally simpler than SQP methods. The
low-memory requirements and simple implementation make our method particularly
suited for embedded NMPC applications
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