Vehicle Motion Planning with Safe Invariant Set Construction
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing path planning methods for vehicles struggle to guarantee operational safety and performance over long time scales due to disturbances and modeling errors, particularly in environments with complex constraints and uncertainties, leading to challenges in incorporating safety mechanisms without sacrificing computational efficiency.
Innovation Solution
The method computes robust invariant sets using a simplified vehicle model, approximated as convex shapes, to ensure safety by inflating unsafe trajectories into safe sets, which can be implemented as continuous or discrete set-point trajectories, and uses Lyapunov functions to establish stability under disturbances.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If robust invariant sets are computed using detailed vehicle models and disturbance models to guarantee safety, then operational safety is improved, but computational burden increases significantly
Solution Approach 1:
The patent changes the parameters of the vehicle model by using a simplified model that captures essential dynamics while reducing complexity. This allows computation of robust invariant sets without the full computational burden of detailed models, maintaining safety guarantees through carefully selected model parameters that represent disturbance effects.
Solution Approach 2:
The patent extracts only the critical components needed for safety analysis from the full vehicle model and disturbance models. By separating the essential safety-critical dynamics from less critical details, the method computes invariant sets with reduced computational effort while preserving safety guarantees for the extracted essential system behavior.
2Productivity
If motion plans are computed over long time horizons to improve mission efficiency, then productivity is improved, but accuracy of disturbance prediction deteriorates
Solution Approach 1:
The patent performs preliminary computation of robust invariant sets using a simplified vehicle model before executing long-horizon motion plans. By pre-computing the invariant sets that capture disturbance effects, the system can then execute efficient long-horizon plans without needing accurate disturbance predictions at each future time step, as the invariant sets provide built-in safety margins.
Solution Approach 2:
The patent segments the motion planning problem into two parts: (1) computation of robust invariant sets using simplified models, and (2) execution of long-horizon motion plans based on these invariant sets. This segmentation allows long time horizons to be used for productivity while the invariant set computation handles the complexity of disturbance effects separately.
3Reliability
If safety constraints are incorporated into motion planning optimization to guarantee operational safety, then reliability is improved, but computational performance deteriorates
Solution Approach 1:
The patent performs preliminary computation of robust invariant sets that encode safety constraints before the motion planning optimization. By pre-computing these invariant sets using simplified models, the actual motion planning optimization only needs to ensure trajectories remain within these pre-computed safe regions, significantly reducing the computational burden of incorporating safety constraints.
Solution Approach 2:
The robust invariant sets act as an intermediary between the safety requirements and the motion planning optimization. Instead of directly incorporating complex safety constraints into the optimization, the invariant sets serve as a mediator that translates safety requirements into geometric regions, making the optimization computationally more efficient while maintaining safety guarantees.
Data Source
Figure 1A
Figure 1B
Figure 1C
AI summary
A system and/or a method for controlling the movement of a vehicle in a constrained environment subject to a disturbed vehicle model including uncertainty on the dynamics governing the movement of the vehicle, collects a feedback signal indicative of a state of the vehicle and a setpoint for controlling the vehicle according to a task and determine a robust invariant set centered on the setpoint for the operation of the vehicle in an unconstrained environment using the disturbed vehicle model. The robust invariant set is inflated equally in all directions until a termination condition defined by the constraint environment is met to produce a safe invariant set enabling control of the operation of the vehicle according to the task while maintaining the state of the vehicle within the safe invariant set.