Jon Arrizabalaga

Tim Salzmann, Elia Kaufmann, Jon Arrizabalaga et al.

Model Predictive Control (MPC) has become a popular framework in embedded control for high-performance autonomous systems. However, to achieve good control performance using MPC, an accurate dynamics model is key. To maintain real-time operation, the dynamics models used on embedded systems have been limited to simple first-principle models, which substantially limits their representative power. In contrast to such simple models, machine learning approaches, specifically neural networks, have been shown to accurately model even complex dynamic effects, but their large computational complexity hindered combination with fast real-time iteration loops. With this work, we present Real-time Neural MPC, a framework to efficiently integrate large, complex neural network architectures as dynamics models within a model-predictive control pipeline. Our experiments, performed in simulation and the real world onboard a highly agile quadrotor platform, demonstrate the capabilities of the described system to run learned models with, previously infeasible, large modeling capacity using gradient-based online optimization MPC. Compared to prior implementations of neural networks in online optimization MPC we can leverage models of over 4000 times larger parametric capacity in a 50Hz real-time window on an embedded platform. Further, we show the feasibility of our framework on real-world problems by reducing the positional tracking error by up to 82% when compared to state-of-the-art MPC approaches without neural network dynamics.

Ishaan Mahajan, Jon Arrizabalaga, Andrea Grillo et al.

Semidefinite programming (SDP) provides a principled framework for convex relaxations of nonconvex geometric constraints in motion planning, yet existing solvers are too computationally expensive for real-time control, particularly on resource-constrained embedded systems. To address this gap, we introduce TinySDP, the first semidefinite programming solver designed for embedded systems, enabling real-time model-predictive control (MPC) on microcontrollers for problems with nonconvex obstacle constraints. Our approach integrates positive-semidefinite cone projections into a cached-Riccati-based ADMM solver, leveraging computational structure for embedded tractability. We pair this solver with an a posteriori rank-1 certificate that converts relaxed solutions into explicit geometric guarantees at each timestep. On challenging benchmarks, e.g., cul-de-sac and dynamic obstacle avoidance scenarios that induce failures in local methods, TinySDP achieves collision-free navigation with up to 73% shorter paths than state-of-the-art baselines. We validate our approach on a Crazyflie quadrotor, demonstrating that semidefinite constraints can be enforced at real-time rates for agile embedded robotics.

Jon Arrizabalaga, Zachary Manchester

This paper introduces a new method for solving quadratic programs using primal-dual interior-point methods. Instead of handling complementarity as an explicit equation in the Karush-Kuhn-Tucker (KKT) conditions, we ensure that complementarity is implicitly satisfied by construction. This is achieved by introducing an auxiliary variable and relating it to the duals and slacks via a retraction map. Specifically, we prove that the softplus function has favorable numerical properties compared to the commonly used exponential map. The resulting KKT system is guaranteed to be spectrally bounded, thereby eliminating the most pressing limitation of primal-dual methods: ill-conditioning near the solution. These attributes facilitate the solution of the underlying linear system, either by removing the need to compute factorizations at every iteration, enabling factorization-free approaches like indirect solvers, or allowing the solver to achieve high accuracy in low-precision arithmetic. Consequently, this novel perspective opens new opportunities for interior-point methods, especially for solving large-scale problems to high precision.

Lukas Pries, Jon Arrizabalaga, Zachary Manchester et al.

This paper presents a numerical solver for computing continuous trajectories in non-convex environments. Our approach relies on a customized implementation of the Alternating Direction Method of Multipliers (ADMM) built upon two key components: First, we parameterize trajectories as polynomials, allowing the primal update to be computed in closed form as a minimum-control-effort problem. Second, we introduce the concept of a spatio-temporal allocation graph based on a mixed-integer formulation and pose the slack update as a shortest-path search. The combination of these ingredients results in a solver with several distinct advantages over the state of the art. By jointly optimizing over both discrete spatial and continuous temporal domains, our method accesses a larger search space than existing decoupled approaches, enabling the discovery of superior trajectories. Additionally, the solver's structural robustness ensures reliable convergence from naive initializations, removing the bottleneck of complex warm starting in non-convex environments.

Tim Salzmann, Jon Arrizabalaga, Joel Andersson et al.

While real-world problems are often challenging to analyze analytically, deep learning excels in modeling complex processes from data. Existing optimization frameworks like CasADi facilitate seamless usage of solvers but face challenges when integrating learned process models into numerical optimizations. To address this gap, we present the Learning for CasADi (L4CasADi) framework, enabling the seamless integration of PyTorch-learned models with CasADi for efficient and potentially hardware-accelerated numerical optimization. The applicability of L4CasADi is demonstrated with two tutorial examples: First, we optimize a fish's trajectory in a turbulent river for energy efficiency where the turbulent flow is represented by a PyTorch model. Second, we demonstrate how an implicit Neural Radiance Field environment representation can be easily leveraged for optimal control with L4CasADi. L4CasADi, along with examples and documentation, is available under MIT license at https://github.com/Tim-Salzmann/l4casadi

Jon Arrizabalaga, Niels van Duijkeren, Markus Ryll et al.

Differential drive mobile robots often use one or more caster wheels for balance. Caster wheels are appreciated for their ability to turn in any direction almost on the spot, allowing the robot to do the same and thereby greatly simplifying the motion planning and control. However, in aligning the caster wheels to the intended direction of motion they produce a so-called bore torque. As a result, additional motor torque is required to move the robot, which may in some cases exceed the motor capacity or compromise the motion planner's accuracy. Instead of taking a decoupled approach, where the navigation and disturbance rejection algorithms are separated, we propose to embed the caster wheel awareness into the motion planner. To do so, we present a caster-wheel-aware term that is compatible with MPC-based control methods, leveraging the existence of caster wheels in the motion planning stage. As a proof of concept, this term is combined with a a model-predictive trajectory tracking controller. Since this method requires knowledge of the caster wheel angle and rolling speed, an observer that estimates these states is also presented. The efficacy of the approach is shown in experiments on an intralogistics robot and compared against a decoupled bore-torque reduction approach and a caster-wheel agnostic controller. Moreover, the experiments show that the presented caster wheel estimator performs sufficiently well and therefore avoids the need for additional sensors.

Jon Arrizabalaga, Markus Ryll

Minimum-time navigation within constrained and dynamic environments is of special relevance in robotics. Seeking time-optimality, while guaranteeing the integrity of time-varying spatial bounds, is an appealing trade-off for agile vehicles, such as quadrotors. State of the art approaches, either assume bounds to be static and generate time-optimal trajectories offline, or compromise time-optimality for constraint satisfaction. Leveraging nonlinear model predictive control and a path parametric reformulation of the quadrotor model, we present a real-time control that approximates time-optimal behavior and remains within dynamic corridors. The efficacy of the approach is evaluated according to simulated results, showing itself capable of performing extremely aggressive maneuvers as well as stop-and-go and backward motions.