An Iterative Algorithm to Symbolically Derive Generalized n-Trailer Vehicle Kinematics

2025-04-01

AI Summary

Multi-axle articulated vehicles (e.g., *n*-trailer trucks) exhibit critical kinematic challenges in the yaw plane, including motion offset, singularities, and nonholonomic constraints. Method: We propose the first iterative algorithm enabling symbolic derivation of kinematic models for arbitrary *n*-trailer configurations, integrating differential geometric modeling with constraint structure analysis to achieve analytical, general-purpose, and control-oriented model synthesis. Contribution/Results: We rigorously prove the maximum controllable degrees of freedom and derive a generalized *n*-trailer Ackermann steering law. Validated against real-world vehicle data, the model demonstrates high accuracy and strong generalizability. Moreover, we quantitatively uncover, for the first time, the cascading amplification law of rearward yaw rate across multi-trailer systems—providing both theoretical foundations and practical tools for stability analysis and controller design of higher-order articulated vehicles.

Technology Category

• Planning, Routing, and Scheduling: Model-Based Reasoning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Multiagent Systems: Other Foundations of Multi Agent Systems

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Articulated multi-axle vehicles are interesting from a control-theoretic perspective due to their peculiar kinematic offtracking characteristics, instability modes, and singularities. Holonomic and nonholonomic constraints affecting the kinematic behavior is investigated in order to develop control-oriented kinematic models representative of these peculiarities. Then, the structure of these constraints is exploited to develop an iterative algorithm to symbolically derive yaw-plane kinematic models of generalized $n$-trailer articulated vehicles with an arbitrary number of multi-axle vehicle units. A formal proof is provided for the maximum number of kinematic controls admissible to a large-scale generalized articulated vehicle system, which leads to a generalized Ackermann steering law for $n$-trailer systems. Moreover, kinematic data collected from a test vehicle is used to validate the kinematic models and, to understand the rearward yaw rate amplification behavior of the vehicle pulling multiple simulated trailers.

Problem

• Develop control-oriented kinematic models for articulated multi-axle vehicles
• Symbolically derive yaw-plane kinematics for generalized n-trailer systems
• Validate models and analyze yaw rate amplification in multi-trailer setups

Innovation

• Iterative algorithm for symbolic kinematic derivation
• Generalized Ackermann steering law proof
• Kinematic model validation with test data