Quadrotor Trajectory Planning via Mixed-Integer Quadratic Programming
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Solution Overview
Problem
Existing multi-rotor aerial vehicles face challenges in generating optimal trajectories for multiple quadrotors in environments with complex obstacles, particularly in ensuring collision avoidance and smooth transitions, due to the high-dimensional search space and complexity of planning for multiple vehicles.
Innovation Solution
The use of mixed-integer quadratic programs (MIQPs) with integer constraints to enforce collision avoidance and optimize trajectory planning, allowing for piece-wise smooth polynomial functions to ensure continuity and safety, and weighting factors to manage vehicle interactions and goal assignments.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional trajectory planning methods are used for multiple quadrotors, then the search space dimension becomes excessively high, but the planning complexity and computational time increase significantly
Solution Approach 1:
The patent segments the high-dimensional trajectory planning problem into lower-dimensional subproblems by introducing integer constraints that discretize the search space. This segmentation allows the use of mixed-integer quadratic programming (MIQP) to break down the complex planning task into manageable components, reducing overall planning complexity while maintaining trajectory optimality.
Solution Approach 2:
The patent changes the parameter representation by introducing integer variables to enforce collision avoidance constraints. This parameter transformation converts the continuous trajectory optimization into a mixed-integer quadratic program, which reduces the effective search space dimension and computational complexity while preserving the ability to find optimal trajectories.
2Reliability
If continuous smooth trajectories are generated for multiple vehicles, then collision avoidance becomes difficult to enforce, but computational complexity increases
Solution Approach 1:
The patent introduces integer constraints as intermediary elements that mediate between trajectory smoothness and collision avoidance. These binary variables act as switches that enforce safety constraints without requiring complex continuous optimization, thereby ensuring collision avoidance while keeping computational complexity manageable through MIQP formulation.
3Productivity
If the search space dimension is reduced for multi-vehicle planning, then computational efficiency improves, but trajectory smoothness may be compromised
Solution Approach 1:
The patent changes the mathematical formulation by using piecewise polynomial functions with integer constraints. This parameter transformation allows the MIQP solver to efficiently find optimal trajectories that satisfy both smoothness requirements (through polynomial continuity constraints) and collision avoidance (through integer variables), achieving both planning efficiency and trajectory precision simultaneously.
Data Source
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AI summary
A system and method is described for controlling flight trajectories of at least two flying vehicles towards goal positions. The system includes at least two flying vehicles with onboard inertial measurement units for determining and updating orientation, angular velocities, position and linear velocities of the at least two flying vehicles, a motion capture system to detect current position and velocity of each of the at least two flying vehicles, and a base controller in communication with the motion capture system and in communication with the plurality of flying vehicles. The base controller calculates for each of the flying vehicles, at predetermined intervals of time, optimum trajectory paths using piece-wise smooth polynomial functions, applying weighting factors, and enforcing overlap constraints.