Two-dimensional Spatial Optimization for Electric Motorcycle Powertrain Elements using Mixed-integer Programming

TL;DR

The paper tackles the challenge of optimally placing electric motorcycle powertrain elements within tight packaging by formulating a two-dimensional, near-continuous orientation design problem as a mixed-integer quadratic program. It introduces a comprehensive modeling framework that handles irregular subsystem shapes via cluster-based subsystems, enforces non-overlap with SAT, and linearizes trigonometric and product terms through a suite of techniques. The approach is demonstrated on single- and dual-motor topologies, showing that incremental subsystem complexity improves handling and yields up to $2.5\%$ better performance than benchmarks, while maintaining tractable computation times. Overall, the work advances spatial powertrain design for compact vehicles by enabling irregular geometries and precise orientation control within a rigorous optimization framework, with potential impact on TCO and ride dynamics in electric motorcycles.

Abstract

This study presents a framework for optimizing the two-dimensional (2D) placement of electric motorcycle powertrain elements, accounting for the position, the orientation and geometric irregularities. Specifically, we construct a 2D placement model at the component level in which we include near-continuous rotation of components and allow for irregular subsystem geometries to make optimal use of the limited design space. Second, we introduce linearization techniques for the trigonometric constraints and formulate the placement problem as a mixed-integer quadratic program (MIQP). Finally, we demonstrate our framework on two electric motorcycle powertrain topologies and study the influence of the geometry complexity on the placement solutions. The results show that gradually increasing complexity leads to more manageable computation times and higher the complexity solution improves handling performance by 2.5% compared to the benchmark placement found in existing electric motorcycles.

Figures (5)

• Figure 1: Overview of the integrated framework for electric motorcycles. The workflow begins with the generation of a set of feasible topologies. In the second stage, the optimal energy consumption of each topology is determined, incorporating a modified Pontryagin’s Minimum Principle to derive the optimal control policy. The final stage optimizes the component placement to enhance handling, while maintaining optimal energy consumption.
• Figure 2: Visualization of the SAT applied to two rectangular objects. In case (\ref{['fig: SAT-demo-failed']}), condition 1 in \ref{['eq: 2D-SAT-rec']} fails, as the length of the projected center vector $\vec{v}_{\mathfrak{d},\mathfrak{z}}$ onto the unit vector $\vec{u}_{1,\mathfrak{d}}$ is shorter than the projected lengths of both objects. In contrast, case (\ref{['fig: SAT-demo-pass']}) illustrates that condition 2 is satisfied, meaning that the objects do not overlap.
• Figure 3: The CoG inactive region of the rear-wheel driven single topology, with the ideal shown in black. The blue region represents the area where the maximum tractive force boundaries are inactive constraints, while the red region indicates where they are active constraints.
• Figure 4: A single $\mathrm{MM}$ topology and its optimal 2D placements with different complexity. The outer dashed black line represents the design space, while the inner dashed black line encloses the feasible region for the mounted motor. The chassis and rider CoGs are marked with $\star$, the overall CoG is represented by a solid black circle, and the CoGs of components and sub-modules are indicated by black dots.
• Figure 5: The topology with a $\mathrm{MM}$ and a $\mathrm{HM_2}$, together with the placement results for battery pack complexity $N_\mathrm{com,BP}$ of 2 and 3.