Target trajectory generation using clothoid curve and vehicle control for obstacle avoidance of automated driving

TAKIYAMA, Takeshi; FUJITA, Junichi · 2020 · DOAJ

DOI: 10.1299/transjsme.19-00174

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Summary

This paper addresses the challenge of generating smooth, drivable target trajectories for automated vehicles to avoid obstacles in real-time. Existing methods, such as mathematical constraints or potential fields, often require trial-and-error parameter tuning and may not adequately account for vehicle drivability. The authors propose using clothoid curves, which are standard in road design and naturally align with vehicle dynamics when steering at a constant angular velocity. The study aims to develop a method to generate these curves passing through specific target points without iterative guessing, and to design a controller that ensures the vehicle tracks this trajectory accurately. The methodology involves two main components: trajectory generation and vehicle control. For trajectory generation, the authors performed numerical analyses to derive the characteristics of clothoid curves. They established approximate linear and quadratic relationships between clothoid parameters (such as the deflection angle and curvature rate) and the chord-arc ratio. Using these relationships, they developed an algorithm to calculate the necessary clothoid parameters to reach a specified endpoint, expanding a unit clothoid segment into a full avoidance trajectory by reflecting and translating the curve segments. For vehicle control, the authors designed an optimal controller using Nonlinear Least Squares Sequential Quadratic Programming (NLSSQP). This controller treats the problem as a 1-input (steering angular velocity) 2-output (lateral position and yaw angle) system, minimizing an objective function that includes lateral deviation, yaw angle deviation, and steering angular acceleration over a prediction horizon. The results demonstrate that the proposed trajectory generation method successfully creates avoidance paths that reach target points with minimal error (0.16% to 0.29%). The generated trajectories maintain smooth curvature changes, ensuring comfort and drivability. Simulation studies on the control system revealed that weighting the steering angular acceleration in the objective function effectively reduces abrupt steering maneuvers. However, excessive weighting led to sluggish responses and failure to track the target trajectory. The optimal balance allowed the vehicle to follow the clothoid path closely while minimizing control effort. The paper also discusses setting target points based on obstacle dimensions, noting that deflection angles exceeding 45 degrees may require additional straight-line segments to remain practical. The significance of this work lies in providing a systematic, non-iterative approach to obstacle avoidance trajectory generation that is inherently compatible with vehicle dynamics. By linking clothoid curve parameters directly to target coordinates, the method eliminates the need for trial-and-error tuning. Furthermore, the NLSSQP-based controller offers a robust solution for underactuated vehicle control, balancing tracking accuracy with smooth steering inputs. This approach enhances the reliability and comfort of automated driving systems during emergency avoidance maneuvers.

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• steering pattern