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

Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation

Many algorithms for control, optimization and estimation in robotics depend on derivatives of the underlying system dynamics, e.g. to compute linearizations, sensitivities or gradient directions. However, we show that when dealing with Rigid Body Dynamics, these derivatives are difficult to derive analytically and to implement efficiently. To overcome this issue, we extend the modelling tool `RobCoGen' to be compatible with Automatic Differentiation. Additionally, we propose how to automatically obtain the derivatives and generate highly efficient source code. We highlight the flexibility and performance of the approach in two application examples. First, we show a Trajectory Optimization example for the quadrupedal robot HyQ, which employs auto-differentiation on the dynamics including a contact model. Second, we present a hardware experiment in which a 6 DoF robotic arm avoids a randomly moving obstacle in a go-to task by fast, dynamic replanning

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

The Control Toolbox - An Open-Source C++ Library for Robotics, Optimal and Model Predictive Control

We introduce the Control Toolbox (CT), an open-source C++ library for efficient modeling, control, estimation, trajectory optimization and Model Predictive Control. The CT is applicable to a broad class of dynamic systems but features interfaces to modeling tools specifically designed for robotic applications. This paper outlines the general concept of the toolbox, its main building blocks, and highlights selected application examples. The library contains several tools to design and evaluate controllers, model dynamical systems and solve optimal control problems. The CT was designed for intuitive modeling of systems governed by ordinary differential or difference equations. It supports rapid prototyping of cost functions and constraints and provides standard interfaces for different optimal control solvers. To date, we support Single Shooting, the iterative Linear-Quadratic Regulator, Gauss-Newton Multiple Shooting and classical Direct Multiple Shooting. We provide interfaces to general purpose NLP solvers and Riccati-based linear-quadratic optimal control solvers. The CT was designed to solve large-scale optimal control and estimation problems efficiently and allows for online control of dynamic systems. Some of the key features to enable fast run-time performance are full compatibility with Automatic Differentiation, derivative code generation, and multi-threading. Still, the CT is designed as a modular framework whose building blocks can also be used for other control and estimation applications such as inverse dynamics control, extended Kalman filters or kinematic planning

Parametric Model Order Reduction of Port-Hamiltonian Systems by Matrix Interpolation

In this paper, parametric model order reduction of linear time-invariant systems by matrix interpolation is adapted to large-scale systems in port-Hamiltonian form. A new weighted matrix interpolation of locally reduced models is introduced in order to preserve the port-Hamiltonian structure, which guarantees the passivity and stability of the interpolated system. The performance of the new method is demonstrated by technical example

Towards a Unified Framework of Efficient Algorithms for Numerical Optimal Robot Control

In the recent past, the wide availability of digital technologies has strongly disrupted many well-established manufacturing techniques and initiated a rapid transformation process in the corresponding industry sectors. However, there are some domains which to date seem to have less profited from digitization. One such domain is building construction and civil engineering. The emerging research field digital fabrication promises a revolution in the construction industry through digitization and robotization of design and manufacturing processes and exhibits a great potential for novel construction technologies and architectural approaches. In this thesis, we introduce the concept of an In situ Fabricator, a versatile and flexible mobile robot dedicated to on-site fabrication. We present a prototype system, show several example applications and motivate the necessity of high-performance optimal control and estimation algorithms for achieving desired construction goals. Such methods enable non-expert users to operate complex robotic systems and are an important building block for advanced autonomous capabilities. For this reason, the main objective of this work is the development of efficient optimal control algorithms and software for high-dimensional robotic systems. We introduce a family of multiple shooting algorithms which exploit the sparsity of the optimal control problem and offer interesting properties for motion planning and nonlinear model predictive control. We derive equality-constrained versions of these algorithms and demonstrate their potential for motion planning and real-time control of non-holonomic vehicles. To facilitate our implementations and speed up our algorithms, in particular to minimize the time required for computing gradient information, we introduce automatic differentiation and code generation for rigid body systems. Our customized solvers combined with derivative code generation and state-of-the-art software engineering form a framework which allows us to perform nonlinear model predictive control for longer time horizons or at higher update rates than other approaches