Motion Trajectory Control With Convex Safety Filtering
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Solution Overview
Problem
Existing motion planning systems for devices in environments with obstacles face significant computational and memory burdens due to non-convex optimization problems, and 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 optimization problem into a convex optimization problem, ensuring hard constraint satisfaction through a convex optimization problem.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If non-convex optimization problem is solved using traditional motion planners (e.g., MIP approach), then optimal motion trajectory can be determined, but significant computational and memory resources are required
Solution Approach 1:
The motion planning problem is segmented into two distinct parts: (1) a learned function (neural network) that generates an initial trajectory without enforcing hard constraints, and (2) a convex optimization-based safety filter that refines the trajectory to satisfy hard constraints. This segmentation allows each component to be optimized independently, reducing overall computational complexity while maintaining reliability.
Solution Approach 2:
The safety filter acts as an intermediary between the learned function and the final trajectory. It takes the initial trajectory from the neural network and transforms it into a constraint-satisfying trajectory through convex optimization, mediating between the computational efficiency of machine learning and the reliability of constraint enforcement.
2Productivity
If machine learning is used to generate motion trajectory, then computational burden is reduced, but hard constraints cannot be enforced reliably
Solution Approach 1:
The learned function performs preliminary action by generating an initial trajectory that approximates the optimal path without worrying about hard constraints. This preliminary trajectory is then refined by the safety filter to ensure constraint satisfaction, allowing the system to benefit from both computational efficiency and reliability.
Solution Approach 2:
The safety filter serves as an intermediary that bridges the gap between the computationally efficient but unreliable learned function and the reliability requirement for hard constraint satisfaction. It transforms the soft-constraint trajectory into a hard-constraint trajectory through convex optimization.
3Loss of time
If MIP approach is used for motion planning, then finite time termination is guaranteed, but computation cost remains significant (NP-Hard)
Solution Approach 1:
The traditional mechanical optimization approach (MIP) is replaced with a hybrid system combining neural network inference (which operates in fixed time regardless of problem complexity) and convex optimization (which is computationally tractable). This substitution replaces the NP-Hard mechanical system with a more efficient computational system.
Data Source
AI summary
The present disclosure provides a system and a method for controlling a 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 feasible or infeasible 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 subject to 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.