Efficient Obstacle Avoidance for Autonomous Vehicles using Linear Parameter-Varying Model Predictive Control with Scheduling Trust Region

Core Concepts

This paper proposes a novel Linear Parameter-Varying Model Predictive Control (LPVMPC) strategy with a scheduling trust region to efficiently solve the obstacle avoidance problem for autonomous vehicles while tracking a reference trajectory.

Abstract

The paper presents a control design for autonomous driving tasks that considers static obstacles. It proposes an LPVMPC strategy that embeds the nonlinear vehicle model into an LPV formulation using a scheduling parameter. This allows for optimal and fast solutions of the underlying convex optimization scheme as a quadratic program (QP).
To ensure the modeling error due to the application of the scheduling parameter predictions does not become significant, the paper introduces the concept of a "scheduling trust region" by enforcing additional soft constraints on the states and inputs. This prevents the infeasibility of the LPVMPC optimization problem that can occur due to poor scheduling parameter predictions.
The paper compares the proposed LPVMPC with trust region to a standard LPVMPC and a Nonlinear MPC (NMPC) in various obstacle avoidance scenarios. The results show that the standard LPVMPC is feasible in only 2 out of 10 scenarios, while the LPVMPC with trust region is feasible in all 10 scenarios. Additionally, the LPVMPC with trust region achieves similar performance to the NMPC while requiring significantly less computation time.

Stats

The vehicle has a mass of 1919 kg and a yaw inertia of 2937 kgm^2.
The front and rear tire cornering stiffnesses are 156 kN/rad and 193 kN/rad, respectively.
The distance from the center of gravity to the front and rear axles are 1.04 m and 1.4 m, respectively.
The sampling time is 0.05 s, and the simulation frequency is 20 Hz.

Quotes

"The enforcement of Eq. (8) in the LPVMPC requires the optimization problem to find the estimated inputs and states, i.e., zi|k, ui|k, in a way that they remain close to the predicted values from the previous time instant, i.e., ˆzi|k, ˆui|k."
"Since the constraint (8) is a soft constraint, we do not require the exact values of ezmax and eumax. In case the bound is too tight, the LPVMPC can use the slack variable to avoid infeasibility."

Key Insights Distilled From

Obstacle Avoidance of Autonomous Vehicles: An LPVMPC with Scheduling Trust Region

by Maryam Nezam... at arxiv.org 05-06-2024

https://arxiv.org/pdf/2405.02030.pdf

Deeper Inquiries

How can the proposed LPVMPC with trust region be extended to handle dynamic obstacles

To extend the proposed LPVMPC with trust region to handle dynamic obstacles, the algorithm can be modified to incorporate real-time obstacle detection and tracking. This would involve integrating sensor data to identify the position and movement of dynamic obstacles. The LPVMPC can then adjust the linear obstacle avoidance constraint dynamically based on the updated obstacle information. By continuously updating the parameters of the linear constraint, the vehicle can navigate around dynamic obstacles while following the reference trajectory. Additionally, the LPVMPC can incorporate predictive modeling to anticipate the future positions of dynamic obstacles and adjust the constraints accordingly to ensure safe navigation.

What are the potential limitations of the linear obstacle avoidance constraint used in the LPVMPC, and how could it be further improved

The linear obstacle avoidance constraint used in the LPVMPC may have limitations in accurately representing the complex shapes and sizes of obstacles. This constraint simplifies obstacles to circles or ellipses, which may not capture the true geometry of obstacles in real-world scenarios. To improve this constraint, advanced obstacle modeling techniques, such as polygonal or spline-based representations, can be implemented to better approximate the shape of obstacles. Additionally, incorporating obstacle classification algorithms can help differentiate between different types of obstacles and apply specific avoidance strategies based on their characteristics. By enhancing the fidelity of obstacle representation, the LPVMPC can improve obstacle avoidance performance and safety.

What other applications beyond autonomous driving could benefit from the scheduling trust region concept introduced in this paper

The scheduling trust region concept introduced in this paper can benefit various applications beyond autonomous driving that involve predictive modeling and real-time decision-making. Some potential applications include:

Robotics: In robotic systems, the scheduling trust region concept can be applied to optimize motion planning and obstacle avoidance strategies. Robots can use predictive modeling to anticipate changes in the environment and adjust their trajectories accordingly, ensuring safe and efficient operation.
Industrial Automation: Manufacturing processes can benefit from scheduling trust regions to optimize production schedules and resource allocation. By incorporating predictive modeling and trust regions, industrial systems can adapt to changing demands and constraints in real-time.
Healthcare: Patient monitoring and treatment planning can utilize scheduling trust regions to adjust treatment protocols based on real-time data and predictive models. This can improve patient outcomes and optimize healthcare resource utilization.
Supply Chain Management: Logistics and supply chain operations can benefit from scheduling trust regions to optimize transportation routes, inventory management, and delivery schedules. By incorporating predictive modeling, companies can adapt to changing market conditions and unforeseen events effectively.