[Paper Review] An Efficient B-spline-Based Kinodynamic Replanning Framework for Quadrotors

Wenchao Ding, Wenliang Gao+2 more|arXiv (Cornell University)|Jun 24, 2019

Robotic Path Planning Algorithms42 references4 citations

TL;DR

This paper proposes an efficient B-spline-based kinodynamic replanning framework for quadrotors that ensures dynamically feasible, smooth trajectories under non-static initial conditions. By combining a novel B-spline-based kinodynamic search with elastic optimization, the method achieves real-time, low-cost trajectory planning while guaranteeing safety and feasibility through convex optimization and graph aggregation techniques.

ABSTRACT

Trajectory replanning for quadrotors is essential to enable fully autonomous flight in unknown environments. Hierarchical motion planning frameworks, which combine path planning with path parameterization, are popular due to their time efficiency. However, the path planning cannot properly deal with non-static initial states of the quadrotor, which may result in non-smooth or even dynamically infeasible trajectories. In this paper, we present an efficient kinodynamic replanning framework by exploiting the advantageous properties of the B-spline, which facilitates dealing with the non-static state and guarantees safety and dynamical feasibility. Our framework starts with an efficient B-spline-based kinodynamic (EBK) search algorithm which finds a feasible trajectory with minimum control effort and time. To compensate for the discretization induced by the EBK search, an elastic optimization (EO) approach is proposed to refine the control point placement to the optimal location. Systematic comparisons against the state-of-the-art are conducted to validate the performance. Comprehensive onboard experiments using two different vision-based quadrotors are carried out showing the general applicability of the framework.

Motivation & Objective

• To address the limitations of hierarchical motion planning in handling non-static initial states, which can lead to jerky or infeasible trajectories.
• To develop a real-time kinodynamic replanning framework that guarantees dynamical feasibility and safety in unknown environments.
• To overcome the computational inefficiency of sampling-based and nonlinear BVP-based kinodynamic planners for quadrotors.
• To integrate a B-spline-based search with a refinement step that optimizes control points for minimal control effort and time.

Proposed method

• Introduces the efficient B-spline-based kinodynamic (EBK) search algorithm that finds feasible trajectories by optimizing B-spline control points on a spatial grid.
• Defines a novel concept of 'vertex tuple' to simplify the search problem and enable theoretical analysis of the solution space.
• Employs a graph aggregation technique with controllable discretization to reduce computation time while preserving optimality.
• Uses an offline-computable minimum inflation strategy to minimize collision checking during online search.
• Applies elastic optimization (EO) to refine control point placement via convex quadratically constrained quadratic programming (QCQP).
• Integrates the framework into a receding horizon replanner leveraging the local control property of B-splines for real-time adaptation.

Experimental results

Research questions

• RQ1 Can a B-spline-based kinodynamic planner achieve real-time performance while ensuring dynamical feasibility and low control effort for quadrotors with non-zero initial states?
• RQ2 How can the discretization error from grid-based search be effectively compensated to improve trajectory optimality?
• RQ3 What is the impact of graph aggregation and minimum inflation on search efficiency without sacrificing solution quality?
• RQ4 How does the proposed framework compare in performance and robustness to state-of-the-art kinodynamic planners in both simulation and real-world flight?
• RQ5 Can the framework be generalized across different vision-based quadrotor platforms with varying sensing and computational capabilities?

Key findings

• The EBK search algorithm achieves real-time performance by leveraging graph aggregation and minimum inflation, significantly reducing online computation time.
• The elastic optimization step successfully refines control point placement, resulting in trajectories with minimal control effort and improved smoothness.
• Comprehensive comparisons show the proposed framework outperforms state-of-the-art methods in terms of trajectory cost, feasibility, and replanning consistency.
• Onboard experiments on two distinct vision-based quadrotor platforms confirm the framework’s general applicability and robustness in real-world scenarios.
• Theoretical analysis proves the EBK search is complete and optimal with respect to the aggregated graph, ensuring convergence to the best feasible solution under discretization.