Petr Listov PhD Researcher
École polytechnique fédérale de Lausanne Department of Mechanical Engineering
Automatic Control Laboratory Route Cantonale
1015 Lausanne Switzerland petr.listov@epfl.ch www.epfl.ch/labs/la/
PolyMPC: An Efficient Tool for Embedded Model
Predictive Control for Fast Mechatronic Systems
Petr Listov, Michael Spieler, Colin Jones École polytechnique fédérale de Lausanne Nonlinear optimal control and trajectory optimization
methods for Airborne Wind Energy (AWE) systems have been extensively explored in recent years. Very promising results have been shown in generating and subsequent tracking of power optimal flight trajectories in simulation studies. Deployment of these algorithms to research and commercial prototypes poses a new challenge, since the computational power of onboard computers is usually very limited. Here we present a new tool that implements the direct collocation of optimal control problems and a nonlinear optimization solver that is optimized for these challenging embedded applications.
Efficient solvers for real-time optimal control are required to run on embedded hardware with highly constrained computational and memory resources. Most existing solvers are based on second-order methods which are prohibitively expensive for many faster applications. The method presented in this paper overcomes many of these challenges.
A nonlinear solver has been developed that applies a Sequential Quadratic Programming (SQP) strategy using an Alternating Direction Method of Multipliers (ADMM) based Quadratic Program (QP) solver. SQP iteratively solves a series of quadratic sub-problems, which are con-structed using forward mode automatic differentiation for linearization and a damped BFGS variant for Hessian estimation. The descent steps are taken using the line search method on a merit function. Optimization tech-niques such as factorization caching and warm-starting result in efficient iterations.
The solver is implemented as a generic nonlinear solver in the form of a header-only module, which integrates into PolyMPC, an open-source C++ library for real-time Nonlinear Model Predictive Control (available for free at https://github.com/LA-EPFL/polympc). A Cheby-shev pseudospectral collocation-based approximation method is used to efficiently discretize the OCP. We leverage the flexibility of templated C++ with the Eigen linear algebra library to construct a problem spe-cific solver which uses only static memory allocation. The implementation is suitable to solve small sized problems on an ARM Cortex-M7 microcontroller with Floating Point Unit (FPU), which was tested on a simulated path follow-ing problem of a two-line soft-wfollow-ing kite as described in [1]. The computation times on three different platforms is shown in the table below. With 63 optimization variables and 45 nonlinear equality constraints the controller ob-ject uses 83280 bytes of memory when using single pre-cision floating point types.
Platform Solve time [ms] Factor
Intel Core i7 2.8 GHz 5.83 1.0
ARM Cortex-A15 19.21 3.3
ARM Cortex-M7 349.00 59.9
References:
[1] Diwale S., Alessandretti A., Lymperopoulos I., Jones C. N. A Non-linear Adaptive Controller for Airborne Wind Energy Systems. In: American Control Conference: 4101ś4106, IEEE; 2016.
