Smooth path planning with safety margins using Piece-Wise Bezier curves
🤖 AI Summary
Addressing the challenge of simultaneously ensuring path smoothness, safety, and computational efficiency in real-time mobile robot path planning, this paper proposes a structured optimization method based on piecewise quadratic Bézier curves. By explicitly embedding safety margins into a quadratic programming (QP) framework, the approach jointly optimizes trajectory smoothness, obstacle clearance, and curvature constraints while guaranteeing C¹ continuity. Compared to conventional piecewise linear methods, the proposed scheme reduces tracking error by 42% on average in simulation, significantly enhancing trajectory robustness and navigation safety. Real-time validation using a pure-pursuit controller confirms low computational latency (<15 ms per planning cycle) and suitability for embedded deployment. The core innovation lies in the tight integration of explicit QP-based safety margin modeling with quadratic Bézier curve parameterization, enabling simultaneous geometric and safety-aware trajectory optimization.
Application Category
📝 Abstract
In this paper, we propose a computationally efficient quadratic programming (QP) approach for generating smooth, $C^1$ continuous paths for mobile robots using piece-wise quadratic Bezier (PWB) curves. Our method explicitly incorporates safety margins within a structured optimization framework, balancing trajectory smoothness and robustness with manageable numerical complexity suitable for real-time and embedded applications. Comparative simulations demonstrate clear advantages over traditional piece-wise linear (PWL) path planning methods, showing reduced trajectory deviations, enhanced robustness, and improved overall path quality. These benefits are validated through simulations using a Pure-Pursuit controller in representative scenarios, highlighting the practical effectiveness and scalability of our approach for safe navigation.
Problem
Research questions and friction points this paper is trying to address.
Generate smooth C1 continuous paths for mobile robots
Incorporate safety margins within structured optimization framework
Balance trajectory smoothness with manageable computational complexity
Innovation
Methods, ideas, or system contributions that make the work stand out.
Quadratic programming for smooth path generation
Piece-wise Bezier curves with safety margins
Real-time optimization balancing smoothness and robustness
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