Minimum Time Dubins Airplane Paths with Asymmetric Climb Rates

We present a biconvex approach for minimum-time motion planning around convex obstacles that is guaranteed to converge, is anytime, and supports derivative constraints to arbitrary order. We jointly convexify the minimum-time objective and all derivative constraints through a change of variables, and handle collision avoidance via time-varying separating planes, reducing the problem to a biconvex program. This program is solved by alternating between computing maximum-margin separating planes and optimizing the trajectory. By only adding planes for obstacles that the current iterate collides with, the trajectory can jump around obstacles and escape local minima. The method is guaranteed to converge starting from a simple collision-free polygonal curve. In our experiments on drone navigation and dual-arm bin unloading, we find that the proposed method reliably produces high-quality trajectories with computation times comparable to state-of-the-art decomposition-based motion planners, while handling a larger class of problems and being substantially more robust to bad initialization. Project page:https://wernerpe.github.io/bmtp-website/

We present a framework leveraging a novel variant of the model-based diffusion algorithm to minimize the time required for a redundant dual-arm robot configuration to follow a desired relative Cartesian path. Our prior work proposed a bi-level optimization approach for the dual-arm problem, where we derived the analytical solution to the lower-level convex sub-problem and solved the high-level nonconvex problem using a primal-dual approach. However, the gradient-based nature leads to a large computation overhead, and it prohibits directly imposing an $L_{\infty}$ Cartesian error constraint along the joint trajectory due to the sparsity of the gradient. In this work, we propose a diffusion-based framework that relies on probabilistic sampling to tackle the aforementioned challenges in the nonconvex high-level problem, leading to a 35x reduction in the runtime and 34% less Cartesian error compared to our prior work.

Motion planning under dynamics constraints, i.e, kinodynamic planning, enables safe robot operation by generating dynamically feasible trajectories that the robot can accurately track. For high-DOF robots such as manipulators, sampling-based motion planners are commonly used, especially for complex tasks in cluttered environments. However, enforcing constraints on robot dynamics in such planners requires solving either challenging two-point boundary value problems (BVPs) or propagating robot dynamics, both of which cause computational bottlenecks that drastically increase planning times. Meanwhile, recent efforts have shown that sampling-based motion planners can generate plans in microseconds using parallelization, but are limited to geometric paths. This paper develops FLASK, a fast parallelized sampling-based kinodynamic motion planning framework for a broad class of differentially flat robot systems, including manipulators, ground and aerial vehicles, and more. Differential flatness allows us to transform the motion planning problem from the original state space to a flat output space, where an analytical time-parameterized solution of the BVP problem can be obtained. A trajectory in the flat output space is then converted back to a closed-form dynamically feasible trajectory in the original state space, enabling fast validation via ``single instruction, multiple data" parallelism. Our framework is fast, exact, and compatible with any sampling-based motion planner, while offering theoretical guarantees on probabilistic exhaustivity and asymptotic optimality based on the closed-form BVP solutions. We extensively verify the effectiveness of our approach in both simulated benchmarks and real experiments with cluttered and dynamic environments, requiring mere microseconds to milliseconds of planning time.