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

2025-08-22

AI Summary

This work addresses the minimum-time motion planning problem for car-like vehicles operating in simplicial complex environments, jointly optimizing trajectory and velocity profile while strictly satisfying kinodynamic constraints—including velocity, acceleration, and steering angle limits. We propose a globally optimal planning framework that (i) formulates the nonconvex fractional program via a mixed-integer bilinear model, (ii) applies variable transformation and McCormick relaxation to obtain a tractable linear relaxation, and (iii) integrates control-space analysis with terrain structure for synergistic optimization, thereby avoiding local minima. Experiments demonstrate that our method achieves a 104× speedup over MPPI and log-MPPI, while consistently generating dynamically feasible, collision-free, and globally near-optimal trajectories—even in complex 3D terrains. The approach significantly improves optimality, feasibility, and computational efficiency compared to state-of-the-art baselines.

Technology Category

• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

This work casts the kinodynamic planning problem for car-like vehicles as an optimization task to compute a minimum-time trajectory and its associated velocity profile, subject to boundary conditions on velocity, acceleration, and steering. The approach simultaneously optimizes 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 analyzes 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 104 times faster while strictly adhering to the specified constraints

Problem

• Computes minimum-time trajectory for car-like vehicles
• Optimizes spatial path and control sequences simultaneously
• Ensures continuous motion from start to target conditions

Innovation

• Mixed-integer linear program optimization
• Simplicial complex environment planning
• Simultaneous path and control optimization