Motion Trajectory Control With ML and Convex Safety Filtering
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Solution Overview
Problem
Motion planning of devices in environments with obstacles is challenging due to non-convex optimization problems, which require significant computational and memory resources, and existing machine learning solutions fail to enforce hard constraints reliably.
Innovation Solution
A system and method using a learned function trained with machine learning to generate an initial trajectory, followed by an optimization-based safety filter to convert the non-convex problem into a convex optimization, ensuring satisfaction of hard constraints through a convex optimization problem.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If non-convex optimization is used to solve motion planning problems, then the trajectory can satisfy hard constraints, but the computational resources and time required increase significantly
Solution Approach 1:
The system performs preliminary action by using a learned function to generate an initial feasible trajectory before optimization. This initial trajectory is generated quickly using machine learning, and then a convex optimization refines it while guaranteeing constraint satisfaction. This two-stage approach avoids the need to solve the full non-convex optimization problem from scratch, significantly reducing computation time while maintaining reliability.
Solution Approach 2:
The learned function acts as an intermediary between the problem definition and the optimization process. It transforms the complex non-convex motion planning problem into a more tractable form by providing a good initial solution, which then serves as the starting point for convex optimization. This intermediary step bridges the gap between quick but unreliable methods and slow but reliable non-convex optimization.
2Loss of time
If machine learning is used to generate trajectories, then computation time is reduced, but hard constraints cannot be reliably enforced
Solution Approach 1:
The system merges two different approaches: a learned function for fast trajectory generation and convex optimization for reliable constraint satisfaction. The learned function provides speed by generating an initial trajectory quickly, while the convex optimization ensures reliability by guaranteeing that hard constraints are satisfied. The combination of these two methods achieves both fast computation and reliable constraint enforcement.
Solution Approach 2:
The system applies local quality by using different methods for different aspects of the problem. The learned function handles the global trajectory shaping where speed is important, while convex optimization handles the local constraint satisfaction where reliability is critical. This division of labor allows each method to excel at what it does best.
3Productivity
If convex optimization is used, then computation is faster, but the solution may deviate significantly from the initial desired trajectory
Solution Approach 1:
The learned function performs preliminary action by generating an initial trajectory that is already close to the desired path. This initial trajectory serves as a warm start for the convex optimization, ensuring that the optimization begins from a point near the optimal solution. As a result, the convex optimization can converge quickly while maintaining high trajectory accuracy, avoiding significant deviations from the initial desired path.
Data Source
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AI summary
The present disclosure provides a system and a method for controlling the motion of a device from an initial state to a target state in an environment having obstacles that form constraints on the motion of the device. The method includes executing a learned function trained with machine learning to generate a trajectory connecting the initial state of the device with the target state of the device while penalizing an extent of violation of at least some of the constraints to produce an initial trajectory. The method further includes solving a convex optimization problem satisfying all the constraints to produce an optimal trajectory that minimizes deviation from the initial trajectory and controlling the motion of the device according to the optimal trajectory.