Related papers: Phasing Through the Flames: Rapid Motion Planning …

To improve safety and energy efficiency, autonomous vehicles are expected to drive smoothly in most situations, while maintaining their velocity below a predetermined speed limit. However, some scenarios such as low road adherence or…

Modern trajectory optimization based approaches to motion planning are fast, easy to implement, and effective on a wide range of robotics tasks. However, trajectory optimization algorithms have parameters that are typically set in advance…

Partial Differential Equations (PDEs) are fundamental tools for modeling physical phenomena, yet most PDEs of practical interest cannot be solved analytically and require numerical approximations. The feasibility of such numerical methods,…

Elliptic Partial Differential Equations (PDEs) play a central role in computing the equilibrium conditions of physical problems (heat, gravitation, electrostatics, etc.). Efficient solutions to elliptic PDEs are also relevant to computer…

The conventional Artificial Potential Field (APF) is fundamentally limited by the local minima issue and its inability to account for the kinematics of moving obstacles. This paper addresses the critical challenge of autonomous collision…

Diffusion and flow matching policies have recently demonstrated remarkable performance in robotic applications by accurately capturing multimodal robot trajectory distributions. However, their computationally expensive inference, due to the…

Autonomous navigation in dynamic environment heavily depends on the environment and its topology. Prior knowledge of the environment is not usually accurate as the environment keeps evolving in time. Since robot is continuously evaluating…

Offline optimal planning of trajectories for redundant robots along prescribed task space paths is usually broken down into two consecutive processes: first, the task space path is inverted to obtain a joint space path, then, the latter is…

We present the AGATE simulation code, a Python-based framework developed primarily for solving the magnetohydrodynamics (MHD) equations while maintaining adaptability to other equation sets. The code employs a modular, object-oriented…

Effective trajectory generation is essential for reliable on-board spacecraft autonomy. Among other approaches, learning-based warm-starting represents an appealing paradigm for solving the trajectory generation problem, effectively…

Trajectory generation for mobile robots in unstructured environments faces a critical dilemma: balancing kinematic smoothness for safe execution with terminal precision for fine-grained tasks. Existing generative planners often struggle…

Building trajectories for biped robot walking is a complex task considering all degrees of freedom (DOFs) commonly bound within the mechanical structure. A typical problem for such robots is the instability produced by violent transitions…

Path planning for autonomous vehicles in arbitrary environments requires a guarantee of safety, but this can be impractical to ensure in real-time when the vehicle is described with a high-fidelity model. To address this problem, this paper…

In this series of papers, we present a motion planning framework for planning comfortable and customizable motion of nonholonomic mobile robots such as intelligent wheelchairs and autonomous cars. In Part I, we presented the mathematical…

In this paper, we propose an unfitted finite element method to solve PDE-constrained shape optimization problems via shape gradient flow. The shape gradient flow system consists of the state equation, the adjoint equation, the velocity…

Partial differential equation (PDE)-constrained optimization arises in many scientific and engineering domains, such as energy systems, fluid dynamics and material design. In these problems, the decision variables (e.g., control inputs or…

We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…

We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising…

Physics-constrained generative modeling aims to produce high-dimensional samples that are both physically consistent and distributionally accurate, a task that remains challenging due to often conflicting optimization objectives. Recent…

In many robotic tasks, such as autonomous drone racing, the goal is to travel through a set of waypoints as fast as possible. A key challenge for this task is planning the time-optimal trajectory, which is typically solved by assuming…