Mobile Robot Trajectory Planning With Two-Stage Optimization
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Solution Overview
Problem
Conventional non-linear constrained optimization methods for autonomous vehicle planning often suffer from slow convergence and a tendency to settle on local optima, particularly as the complexity of cost functions and robot models increases, leading to suboptimal trajectory planning.
Innovation Solution
A two-stage optimization approach is employed, where a first stage uses a simpler linear cost function and dynamics model to initialize a second stage with a more complex non-linear model, reducing the likelihood of local optima and improving convergence to a globally optimal solution.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If non-linear constrained optimization is used for trajectory planning, then the planning can handle complex cost functions and robot models, but convergence becomes slow and uncertain and the solution may converge to local optima
Solution Approach 1:
The optimization problem is divided into two separate stages: a first optimization stage and a second optimization stage. The first stage uses a simplified cost function and provides an initial solution, while the second stage refines this solution using the full complex cost function. This segmentation allows each stage to focus on specific aspects of the problem, improving overall convergence reliability while maintaining the ability to handle complex planning scenarios.
Solution Approach 2:
The first optimization stage performs preliminary optimization using a simplified model and cost function to generate an initial solution before the second stage begins. This preliminary action provides a good starting point for the subsequent optimization, reducing the likelihood of converging to local optima and improving the reliability of finding the global optimum in the second stage.
2Measurement precision
If a complex cost function and robot model are used in optimization, then the trajectory planning becomes more accurate, but the optimization time increases significantly
Solution Approach 1:
The computation is segmented into two stages where the first stage uses a simplified model requiring less computation time to generate an initial solution, and the second stage refines this solution with the full complex model. This segmentation reduces the total optimization time while maintaining high accuracy by applying the complex model only to refine an already-good initial solution rather than optimizing from scratch.
Solution Approach 2:
The first optimization stage performs preliminary computation using a simplified cost function and robot model to generate an initial trajectory quickly. This preliminary action eliminates the need for the second stage to start from a random or poor initial solution, significantly reducing the computation time required to achieve high-accuracy trajectory planning with the full complex model.
Data Source
AI summary
A computer-implemented method of determining control actions for controlling a mobile robot comprises: receiving a set of scenario description parameters describing a scenario and a desired goal for the mobile robot therein; in a first constrained optimization stage, applying a first optimizer to determine a first series of control actions that substantially globally optimizes a preliminary cost function for the scenario, the preliminary cost function based on a first computed trajectory of the mobile robot, as computed by applying a preliminary robot dynamics model to the first series of control actions, and in a second constrained optimization stage, applying a second optimizer to determine a second series of control actions that substantially globally optimizes a full cost function for the scenario, the full cost function based on a second computed trajectory of the mobile robot, as computed by applying a full robot dynamics model to the second series of control actions; wherein initialization data of at least one of the first computed trajectory and the first series of control actions is used to initialize the second optimizer for determining the second series of control actions, and wherein the preliminary robot dynamic model approximates the full robot dynamics model, the cost functions embody similar objectives to each encourage achievement of the desired goal, and both are optimized with respect to similar hard constraints, such that the initialization data guides the second optimizer to the substantially globally-optimal second series of control actions.