Trajectory Optimization via Closed-Form Integration
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Solution Overview
Problem
Existing methods for generating optimized trajectories for autonomous vehicles are inefficient, particularly in resource-limited or time-limited environments, as they often require separate optimization of vehicle velocities and steering angles, leading to increased processing power and memory requirements.
Innovation Solution
The use of closed-form numerical integration in route-relative coordinates allows for simultaneous optimization of lateral and longitudinal dynamics using a single algorithm, such as the projected stage-wise Newton method, which reduces the number of iterations needed to generate optimized trajectories.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If separate optimization of vehicle velocities and steering angles is used, then trajectory optimization can be achieved, but processing power and memory requirements increase
Solution Approach 1:
The patent combines separate optimization of vehicle velocities and steering angles into a unified trajectory optimization algorithm. By representing both lateral dynamics (steering angles) and longitudinal dynamics (velocities) in a single algorithm using closed-form numerical integration, the system optimizes both simultaneously, reducing computational overhead and resource requirements while maintaining optimization quality.
2Reliability
If separate optimization of vehicle velocities and steering angles is used, then trajectory optimization can be achieved, but computation time increases
Solution Approach 1:
The patent merges separate optimization processes into a single unified algorithm that simultaneously determines both velocity and steering angle trajectories. This integration eliminates the need for multiple sequential optimization passes, reducing computation time while achieving the same optimization quality through closed-form numerical integration.
Solution Approach 2:
The patent uses closed-form numerical integration to pre-compute and represent the relationship between steering angles, velocities, and trajectory parameters. By establishing these mathematical relationships in advance through closed-form solutions, the system avoids iterative computation during real-time optimization, significantly reducing computation time.
3Productivity
If closed-form numerical integration is used for simultaneous optimization, then processing efficiency improves, but algorithm complexity increases
Solution Approach 1:
The patent replaces iterative numerical optimization methods with closed-form numerical integration. By substituting the mechanical iterative process with a closed-form mathematical solution, the system achieves higher processing efficiency. The closed-form approach directly computes the optimal trajectory parameters without requiring multiple iterative passes, reducing algorithmic complexity in practice despite the advanced mathematics involved.
Data Source
AI summary
Techniques are discussed for generating and optimizing a trajectory using closed-form numerical integration in route-relative coordinates. A decision planner component of an autonomous vehicle, for example, can receive or generate a reference trajectory, which may correspond to an ideal route for an autonomous vehicle to traverse through an environment, such as a center of a road segment. Lateral dynamics (e.g., steering angles, curvature values of trajectory segments) and longitudinal dynamics (e.g., velocity and acceleration) can be represented in a single algorithm such that optimizing the reference trajectory (e.g., based on loss functions or costs) can substantially simultaneously optimize the lateral dynamics and longitudinal dynamics in a single convergence operation. In some cases, the trajectory can be used to control the autonomous vehicle to traverse an environment.