Exact Wavefront Propagation for Globally Optimal One-to-All Path Planning on 2D Cartesian Grids

This paper introduces an efficient $\mathcal{O}(n)$ compute and memory complexity algorithm for globally optimal path planning on 2D Cartesian grids. Unlike existing marching methods that rely on approximate discretized solutions to the Eikonal equation, our approach achieves exact wavefront propagation by pivoting the analytic distance function based on visibility. The algorithm leverages a dynamic-programming subroutine to efficiently evaluate visibility queries. Through benchmarking against state-of-the-art any-angle path planners, we demonstrate that our method outperforms existing approaches in both speed and accuracy, particularly in cluttered environments. Notably, our method inherently provides globally optimal paths to all grid points, eliminating the need for additional gradient descent steps per path query. The same capability extends to multiple starting positions. We also provide a greedy version of our algorithm as well as open-source C++ implementation of our solver.

An Efficient Solution to the 2D Visibility Problem in Cartesian Grid Maps and its Application in Heuristic Path Planning

This paper introduces a novel, lightweight method to solve the visibility problem for 2D grids. The proposed method evaluates the existence of lines-of-sight from a source point to all other grid cells in a single pass with no preprocessing and independently of the number and shape of obstacles. It has a compute and memory complexity of $\mathcal{O}(n)$, where $n = n_{x}\times{} n_{y}$ is the size of the grid, and requires at most ten arithmetic operations per grid cell. In the proposed approach, we use a linear first-order hyperbolic partial differential equation to transport the visibility quantity in all directions. In order to accomplish that, we use an entropy-satisfying upwind scheme that converges to the true visibility polygon as the step size goes to zero. This dynamic-programming approach allows the evaluation of visibility for an entire grid orders of magnitude faster than typical ray-casting algorithms. We provide a practical application of our proposed algorithm by posing the visibility quantity as a heuristic and implementing a deterministic, local-minima-free path planner, setting apart the proposed planner from traditional methods. Lastly, we provide necessary algorithms and an open-source implementation of the proposed methods.

IMPACT: A Toolchain for Nonlinear Model Predictive Control Specification, Prototyping, and Deployment

We present IMPACT, a flexible toolchain for nonlinear model predictive control (NMPC) specification with automatic code generation capabilities. The toolchain reduces the engineering complexity of NMPC implementations by providing the user with an easy-to-use application programming interface, and with the flexibility of using multiple state-of-the-art tools and numerical optimization solvers for rapid prototyping of NMPC solutions. IMPACT is written in Python, users can call it from Python and MATLAB, and the generated NMPC solvers can be directly executed from C, Python, MATLAB and Simulink. An application example is presented involving problem specification and deployment on embedded hardware using Simulink, showing the effectiveness and applicability of IMPACT for NMPC-based solutions.