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A Real-Time Approach for Chance-Constrained Motion Planning with Dynamic Obstacles (2001.08012v2)

Published 22 Jan 2020 in cs.RO and math.OC

Abstract: Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an obstacle's space: a polyhedron, such as a cuboid, or a nonlinear differentiable surface, such as an ellipsoid. The former approach relies on disjunctive programming, which has a relatively high computational cost that grows exponentially with the number of obstacles. The latter approach needs to be linearized locally to find a tractable evaluation of the chance constraints, which dramatically reduces the remaining free space and leads to over-conservative trajectories or even unfeasibility. In this work, we present a hybrid approach that eludes the pitfalls of both strategies while maintaining the original safety guarantees. The key idea consists in obtaining a safe differentiable approximation for the disjunctive chance constraints bounding the obstacles. The resulting nonlinear optimization problem is free of chance constraint linearization and disjunctive programming, and therefore, it can be efficiently solved to meet fast real-time requirements with multiple obstacles. We validate our approach through mathematical proof, simulation and real experiments with an aerial robot using nonlinear model predictive control to avoid pedestrians.

Citations (67)

Summary

  • The paper introduces a hybrid method that uses differentiable approximations of disjunctive chance constraints to balance safety and efficiency.
  • It leverages a nonlinear optimization framework to significantly lower computational demands while maintaining precise collision avoidance in dynamic settings.
  • Extensive simulations and aerial robot experiments validate its approach, demonstrating reduced conservatism and effective trajectory control.

A Real-Time Approach for Chance-Constrained Motion Planning with Dynamic Obstacles

The paper addresses a prevalent challenge in robotics: the need for effective motion planning in environments with dynamic and uncertain obstacles, typically encountered in applications involving autonomous vehicles such as drones or self-driving cars. Existing strategies primarily utilize geometric constructs like polyhedrons or nonlinear differentiable surfaces to define safe bounds around obstacles, both of which present computational challenges that limit their practicality in real-time scenarios. This work proposes a hybrid approach that combines elements from both strategies to provide a more computationally efficient solution while preserving the safety guarantees offered by traditional methods.

Hybrid Approach to Motion Planning

Traditional motion planning solutions either leverage polyhedral (linear) representations requiring disjunctive programming, which is computationally expensive, or nonlinear surface approximations that necessitate local linearization, leading to overly conservative trajectories and potential infeasibility. This paper introduces a hybrid methodology that encapsulates dynamic obstacles using a differentiable approximation of disjunctive chance constraints. This formulation ensures safety while avoiding the pitfalls of computational intensity and conservatism.

Methodology and Theoretical Contributions

The hybrid approach employs a nonlinear optimization framework, which can be solved efficiently with existing solvers. The primary theoretical contributions include:

  • Disjunctive Chance Constraints: A safe differentiable approximation reduces conservatism present in existing approaches, enabling tighter bounds on collision probabilities.
  • Computational Efficiency: The reformulated problem fits within a nonlinear programming framework, markedly improving computation speed to meet real-time requirements.

The authors provide validation through mathematical proofs, simulations, and actual experiments using an aerial robot.

Practical Implications and Validation

Empirical validation is achieved through simulation and real-world experiments where aerial robots navigate environments populated with pedestrians. The proposed approach demonstrates reduced conservatism compared to state-of-the-art methods and maintains computational efficiency, crucial for applications requiring real-time response. Specifically, it is tested with model predictive control (MPC) implementations on a DJI-M100 quadrotor. Statistical evaluations show low collision risk and efficient trajectory planning, indicating potential for scalability in more complex scenarios.

Anticipated Developments in AI and Robotics

The implications for future work suggest improvements in risk allocation methods and enhanced closed-loop constraint satisfaction strategies, further reducing conservativeness while maintaining safety. Additionally, the approach could be adapted for various robotic platforms and objectives beyond mere collision avoidance, including perception and energy optimization in dynamic environments.

This paper contributes notably to the active field of motion planning under uncertainty, presenting a viable solution for dynamic environments without sacrificing safety or computational feasibility. The developed methodology holds promise for deployment in real-world settings where autonomous systems must make fast and safe decisions amidst unpredictable conditions.

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