Exploiting Chordality in Optimization Algorithms for Model Predictive Control

In this chapter we show that chordal structure can be used to devise efficient optimization methods for many common model predictive control problems. The chordal structure is used both for computing search directions efficiently as well as for distributing all the other computations in an interior-point method for solving the problem. The chordal structure can stem both from the sequential nature of the problem as well as from distributed formulations of the problem related to scenario trees or other formulations. The framework enables efficient parallel computations.Comment: arXiv admin note: text overlap with arXiv:1502.0638

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

FATROP : A Fast Constrained Optimal Control Problem Solver for Robot Trajectory Optimization and Control

Trajectory optimization is a powerful tool for robot motion planning and control. State-of-the-art general-purpose nonlinear programming solvers are versatile, handle constraints in an effective way and provide a high numerical robustness, but they are slow because they do not fully exploit the optimal control problem structure at hand. Existing structure-exploiting solvers are fast but they often lack techniques to deal with nonlinearity or rely on penalty methods to enforce (equality or inequality) path constraints. This works presents FATROP: a trajectory optimization solver that is fast and benefits from the salient features of general-purpose nonlinear optimization solvers. The speed-up is mainly achieved through the use of a specialized linear solver, based on a Riccati recursion that is generalized to also support stagewise equality constraints. To demonstrate the algorithm's potential, it is benchmarked on a set of robot problems that are challenging from a numerical perspective, including problems with a minimum-time objective and no-collision constraints. The solver is shown to solve problems for trajectory generation of a quadrotor, a robot manipulator and a truck-trailer problem in a few tens of milliseconds. The algorithm's C++-code implementation accompanies this work as open source software, released under the GNU Lesser General Public License (LGPL). This software framework may encourage and enable the robotics community to use trajectory optimization in more challenging applications

方策最適化による機会制約付き確率モデル予測制御の高速アルゴリズム

京都大学新制・課程博士博士(情報学)甲第24743号情博第831号新制||情||139(附属図書館)京都大学大学院情報学研究科システム科学専攻(主査)教授 大塚 敏之, 教授 加納 学, 教授 東 俊一学位規則第4条第1項該当Doctor of InformaticsKyoto UniversityDFA

A Convex Feasibility Approach to Anytime Model Predictive Control

This paper proposes to decouple performance optimization and enforcement of asymptotic convergence in Model Predictive Control (MPC) so that convergence to a given terminal set is achieved independently of how much performance is optimized at each sampling step. By embedding an explicit decreasing condition in the MPC constraints and thanks to a novel and very easy-to-implement convex feasibility solver proposed in the paper, it is possible to run an outer performance optimization algorithm on top of the feasibility solver and optimize for an amount of time that depends on the available CPU resources within the current sampling step (possibly going open-loop at a given sampling step in the extreme case no resources are available) and still guarantee convergence to the terminal set. While the MPC setup and the solver proposed in the paper can deal with quite general classes of functions, we highlight the synthesis method and show numerical results in case of linear MPC and ellipsoidal and polyhedral terminal sets.Comment: 8 page