Safety-Critical Trajectory Planning and Control for Dynamic Obstacle Avoidance Using Discrete-Time Control Barrier Functions

Core Concepts

This paper presents a novel framework that integrates iterative model predictive control with discrete-time control barrier functions to generate collision-free trajectories for a robot navigating through tight and dynamically changing environments with both convex and nonconvex obstacles.

Abstract

The paper addresses the challenge of dynamic obstacle avoidance in optimal control and trajectory planning problems, especially in tight environments. Many existing works use control barrier functions (CBFs) to enforce safety constraints, but they often require knowledge of obstacle boundary equations or have slow computational efficiency.
The key contributions of this paper are:

A model predictive control strategy that uses discrete-time high-order control barrier functions (DHOCBFs) to enforce safety-critical constraints. The DHOCBF constraints are obtained from convex polyhedra generated in sequential grid maps, without the need to know the boundary equations of obstacles.

A novel optimal control framework that integrates convex optimization, sequential grid maps, and a rapid path planning algorithm (Jump Point Search) to generate optimal and safe trajectories in dynamic environments.

Numerical examples demonstrating the proposed framework's ability to enable a unicycle robot to navigate safely and efficiently through tight and dynamic environments with convex or nonconvex obstacles, using rapid control and trajectory generation.

The paper first introduces the preliminaries on DHOCBFs and Jump Point Search. It then presents the methodology, including the iterative MPC-DHOCBF algorithm, dynamic path planning, path reconstruction, linearization of dynamics, and the formulation of the convex finite-time constrained optimal control problem.
The case studies and simulations validate the effectiveness of the proposed approach. The algorithm demonstrates fast computation speed (less than 0.2 seconds per step) and a high obstacle avoidance success rate (over 85%) in various scenarios with different numbers of obstacles and horizon lengths.

Stats

The unicycle model is discretized with a time interval of ∆t = 0.01.
The state and input constraints are: -50 ≤ x, y ≤ 50, -10 ≤ θ ≤ 10, -40 ≤ v ≤ 40, and -15 ≤ u1, u2 ≤ 15.
The initial state is [-35, -35, θ0, 25]^T and the target state is [45, 45, θtsim, 25]^T.

Quotes

"We propose a novel framework to the iterative MPC with DHOCBFs that can generate a collision-free trajectory and computes fast."
"We show through numerical examples that the proposed framework enables a unicycle robot to navigate with safe maneuvers through tight and dynamic environments with convex or nonconvex shape obstacles using rapid control and trajectory generation."

Key Insights Distilled From

Safety-Critical Planning and Control for Dynamic Obstacle Avoidance Using Control Barrier Functions

by Shuo Liu,Yih... at arxiv.org 03-29-2024

https://arxiv.org/pdf/2403.19122.pdf

Deeper Inquiries

How can the proposed framework be extended to handle scenarios where the future information about dynamic obstacles in grid maps is unknown

To handle scenarios where the future information about dynamic obstacles in grid maps is unknown, the proposed framework can be extended by incorporating real-time sensing and perception capabilities. By integrating sensors such as LiDAR, cameras, or radar systems, the robot can gather information about its surroundings and dynamically update the grid map with obstacle positions and movements. This real-time data can then be used to adjust the trajectory planning and obstacle avoidance strategies on the fly. Additionally, machine learning algorithms can be employed to predict the potential trajectories of dynamic obstacles based on historical data, enabling the robot to proactively plan its path even in the absence of complete future information.

What other types of systems, beyond the unicycle model, can benefit from the integration of the iterative MPC-DHOCBF approach and the grid-based path planning algorithm

Beyond the unicycle model, various types of systems can benefit from the integration of the iterative MPC-DHOCBF approach and the grid-based path planning algorithm. Some examples include:

Autonomous Vehicles: Cars, drones, and other autonomous vehicles can utilize this framework for safe navigation in dynamic environments, avoiding both static and moving obstacles.
Industrial Robots: Manufacturing robots operating in complex environments can benefit from the real-time obstacle avoidance capabilities to enhance safety and efficiency.
Aerial Vehicles: UAVs conducting surveillance or delivery missions can use this approach to navigate through urban or cluttered environments while avoiding collisions.
Mobile Robots: Wheeled or legged robots in indoor or outdoor settings can leverage the framework for path planning and obstacle avoidance in crowded spaces.

The key lies in adapting the framework's principles to the specific dynamics and constraints of each system, ensuring safe and efficient operation in diverse scenarios.

Can the computational efficiency of the proposed method be further improved, for example, through parallelization or other optimization techniques

The computational efficiency of the proposed method can be further improved through parallelization and optimization techniques. Here are some strategies to enhance efficiency:

Parallel Computing: Implementing parallel processing techniques can distribute the computational load across multiple cores or processors, enabling faster execution of optimization algorithms and path planning tasks.
Algorithmic Optimization: Fine-tuning the iterative MPC-DHOCBF algorithm by optimizing the solver settings, refining convergence criteria, and streamlining the constraint formulations can improve overall efficiency.
Hardware Acceleration: Utilizing specialized hardware like GPUs or FPGAs for specific computations can accelerate the processing speed, especially for complex optimization problems.
Reduced Horizon Planning: Implementing adaptive horizon strategies where the prediction horizon is dynamically adjusted based on the complexity of the environment can optimize computational resources while maintaining performance.
Caching and Memoization: Storing and reusing intermediate results or precomputed data can reduce redundant calculations and speed up the decision-making process during trajectory planning.

By combining these techniques and continuously refining the implementation, the computational efficiency of the framework can be significantly enhanced, enabling real-time operation in dynamic environments.