On Kinodynamic Global Planning in a Simplicial Complex Environment: A Mixed Integer Approach

<p dir="ltr">This work casts the kinodynamic planning problem for car-like vehicles as an optimisation task to compute a minimum-time trajectory and its associated velocity profile, subject to boundary conditions on velocity, acceleration, and steering. The approach simultaneously optimises both the spatial path and the sequence of acceleration and steering controls, ensuring continuous motion from a specified initial position and velocity to a target end position and velocity. The method analyses the admissible control space and terrain to avoid local minima. The proposed method operates efficiently in simplicial complex environments, a preferred terrain representation for capturing intricate 3D landscapes. The problem is initially posed as a mixed-integer fractional program with quadratic constraints, which is then reformulated into a mixed-integer bilinear objective through a variable transformation and subsequently relaxed to a mixed-integer linear program using McCormick envelopes. Comparative simulations against planners such as MPPI and log-MPPI demonstrate that the proposed approach generates solutions 10^4 times faster while strictly adhering to the specified constraints.</p>