Marcus Greiff

Thomas Lew, Marcus Greiff, John Subosits et al.

Proximal methods such as the Alternating Direction Method of Multipliers (ADMM) are effective at solving constrained quadratic programs (QPs). To tackle infeasible QPs, slack variables are often introduced to ensure feasibility, which changes the structure of the problem, increases its size, and slows down numerical resolution. In this letter, we propose a simple ADMM scheme to tackle QPs with slack variables without increasing the size of the original problem. The only modification is a slightly different projection in the z-update, while the rest of the algorithm remains standard. We prove that the method is equivalent to applying ADMM to the QP with additional slack variables, even though slack variables are not added. Numerical experiments show speedups of the approach.

Alexander Davydov, Franck Djeumou, Marcus Greiff et al.

Combining data-driven models that adapt online and model predictive control (MPC) has enabled effective control of nonlinear systems. However, when deployed on unstable systems, online adaptation may not be fast enough to ensure reliable simultaneous learning and control. For example, a controller on a vehicle executing highly dynamic maneuvers--such as drifting to avoid an obstacle--may push the vehicle's tires to their friction limits, destabilizing the vehicle and allowing modeling errors to quickly compound and cause a loss of control. To address this challenge, we present an active information gathering framework for identifying vehicle dynamics as quickly as possible. We propose an expressive vehicle dynamics model that leverages Bayesian last-layer meta-learning to enable rapid online adaptation. The model's uncertainty estimates are used to guide informative data collection and quickly improve the model prior to deployment. Dynamic drifting experiments on a Toyota Supra show that (i) the framework enables reliable control of a vehicle at the edge of stability, (ii) online adaptation alone may not suffice for zero-shot control and can lead to undesirable transient errors or spin-outs, and (iii) active data collection helps achieve reliable performance.

Gonçalo Dias Pais, Valter Piedade, Moitreya Chatterjee et al.

Several variants of Neural Radiance Fields (NeRFs) have significantly improved the accuracy of synthesized images and surface reconstruction of 3D scenes/objects. In all of these methods, a key characteristic is that none can train the neural network with every possible input data, specifically, every pixel and potential 3D point along the projection rays due to scalability issues. While vanilla NeRFs uniformly sample both the image pixels and 3D points along the projection rays, some variants focus only on guiding the sampling of the 3D points along the projection rays. In this paper, we leverage the implicit surface representation of the foreground scene and model a probability density function in a 3D image projection space to achieve a more targeted sampling of the rays toward regions of interest, resulting in improved rendering. Additionally, a new surface reconstruction loss is proposed for improved performance. This new loss fully explores the proposed 3D image projection space model and incorporates near-to-surface and empty space components. By integrating our novel sampling strategy and novel loss into current state-of-the-art neural implicit surface renderers, we achieve more accurate and detailed 3D reconstructions and improved image rendering, especially for the regions of interest in any given scene.

Emre Adabag, Marcus Greiff, John Subosits et al.

Differentiable model predictive control (MPC) offers a powerful framework for combining learning and control. However, its adoption has been limited by the inherently sequential nature of traditional optimization algorithms, which are challenging to parallelize on modern computing hardware like GPUs. In this work, we tackle this bottleneck by introducing a GPU-accelerated differentiable optimization tool for MPC. This solver leverages sequential quadratic programming and a custom preconditioned conjugate gradient (PCG) routine with tridiagonal preconditioning to exploit the problem's structure and enable efficient parallelization. We demonstrate substantial speedups over CPU- and GPU-based baselines, significantly improving upon state-of-the-art training times on benchmark reinforcement learning and imitation learning tasks. Finally, we showcase the method on the challenging task of reinforcement learning for driving at the limits of handling, where it enables robust drifting of a Toyota Supra through water puddles.

Zhiyong Sun, Marcus Greiff, Anders Robertsson et al.

We consider the problem of cooperative motion coordination for multiple heterogeneous mobile vehicles subject to various constraints. These include nonholonomic motion constraints, constant speed constraints, holonomic coordination constraints, and equality/inequality geometric constraints. We develop a general framework involving differential-algebraic equations and viability theory to determine coordination feasibility for a coordinated motion control under heterogeneous vehicle dynamics and different types of coordination task constraints. If a coordinated motion solution exists for the derived differential-algebraic equations and/or inequalities, a constructive algorithm is proposed to derive an equivalent dynamical system that generates a set of feasible coordinated motions for each individual vehicle. In case studies on coordinating two vehicles, we derive analytical solutions to motion generation for two-vehicle groups consisting of car-like vehicles, unicycle vehicles, or vehicles with constant speeds, which serve as benchmark coordination tasks for more complex vehicle groups. The motion generation algorithm is well-backed by simulation data for a wide variety of coordination situations involving heterogeneous vehicles. We then extend the vehicle control framework to deal with the cooperative coordination problem with time-varying coordination tasks and leader-follower structure. We show several simulation experiments on multi-vehicle coordination under various constraints to validate the theory and the effectiveness of the proposed schemes.

Marcus Greiff, Zhiyong Sun, Anders Robertsson et al.

Controlled invariant set and viability regulation of dynamical control systems have played important roles in many control and coordination applications. In this paper we develop a temporal viability regulation theory for general dynamical control systems, and in particular for control affine systems. The time-varying viable set is parameterized by time-varying constraint functions, with the aim to regulate a dynamical control system to be invariant in the time-varying viable set so that temporal state-dependent constraints are enforced. We consider both time-varying equality and inequality constraints in defining a temporal viable set. We also present sufficient conditions for the existence of feasible control input for the control affine systems. The developed temporal viability regulation theory is applied to mobile vehicle coordination.

Zhiyong Sun, Marcus Greiff, Anders Robertsson et al.

We consider the problem of feasible coordination control for multiple homogeneous or heterogeneous mobile vehicles subject to various constraints (nonholonomic motion constraints, holonomic coordination constraints, equality/inequality constraints etc). We develop a general framework involving differential-algebraic equations and viability theory to describe and determine coordination feasibility for a coordinated motion control under heterogeneous vehicle dynamics and different types of coordination constraints. If a solution exists for the derived differential-algebraic equations and/or inequalities, a heuristic algorithm is proposed for generating feasible trajectories for each individual vehicle. In case studies on coordinating two vehicles, we derive analytical solutions to motion generation for two-vehicle groups consisting of car-like vehicles, unicycle vehicles, or vehicles with constant speeds, which serve as benchmark coordination tasks for more complex vehicle groups. We show several simulation experiments on multi-vehicle coordination under various constraints to validate the theory and the effectiveness of the proposed schemes.