Where You Put the Battery Changes Everything: How Joint Optimization Is Transforming Automotive Design

The Old Way of Building Cars Was Fundamentally Broken

For decades, automotive engineers designed vehicles in a peculiar sequence: first, they figured out how big the engine needed to be, how powerful the battery had to be, and what the transmission should do. Only after all of that was settled—often after years of work—would a separate team of engineers be handed the specifications and told to "make it fit."

This sequential approach made sense when cars were simpler machines. An internal combustion engine went in the front. A fuel tank went in the back. Wheels went at the corners. The constraints were obvious, and the order mattered less.

But modern vehicles are not simple machines. A single electric vehicle might house a battery pack that doubles as structural chassis reinforcement, multiple electric motors distributed across axles, cooling systems that snake through the undercarriage, power electronics that must stay cool while remaining accessible, and suspension components that interact with everything else. Each of these components influences how the others perform. Put the battery higher, and you raise the vehicle's center of gravity, which changes how it handles corners and how much energy you can recover through regenerative braking. Move the motors aft, and you shift where the vehicle wants to accelerate, which affects traction and stability.

The old sequential approach meant engineers were exploring a fundamentally incomplete design space. They were making decisions about component size and performance without knowing where those components would ultimately live inside the vehicle. By the time placement was considered, the major decisions were already locked in.

A team of researchers at Eindhoven University of Technology has spent years developing a different approach. Their framework, which they call SPI2—Spatial Packaging of Interconnected Systems with Physical Interactions—treats placement not as a downstream constraint but as an active design variable that participates in optimization alongside component sizing, structural design, and performance targets. In a series of validation studies, their method found better solutions than exhaustive search while requiring less computation time. More remarkably, it demonstrated that a single design decision—where you put a battery—can ripple through an entire vehicle in ways that reshape optimal powertrain choices. The research appears in a recent preprint published to arXiv (Bückmann, van Kampen, and Hofman, 2026).

The implications extend beyond automotive engineering. Any system where physical components interact through forces, mass distribution, and spatial constraints could benefit from this integrated approach—electric aircraft, industrial robots, marine vessels, or any complex machine where geometry and performance are intertwined.

The Science

The fundamental challenge the researchers confronted was one of integration. Automotive companies have powerful tools for powertrain optimization: algorithms that can size an electric motor, select transmission gear ratios, and balance performance against efficiency. They also have powerful tools for spatial design: software that can pack components into available volume while avoiding collisions and respecting manufacturing constraints.

The problem is that these tools don't talk to each other.

When powertrain engineers optimize motor sizing, they typically make assumptions about vehicle weight and mass distribution. When packaging engineers place components, they work with fixed component specifications. Neither team can see the other's design space, which means neither team can explore the trade-offs that exist at the intersection of their domains.

The researchers' core insight was that these two optimization problems are not independent—they are deeply coupled through physical mechanisms that are well-understood but rarely modeled together.

To understand the coupling, consider what happens when you move a battery pack from its default position to a lower location in the vehicle floor. The vehicle's center of gravity shifts downward and typically rearward. This changes the load distribution across the front and rear axles when the vehicle accelerates or brakes. In a vehicle with rear-wheel-drive and regenerative braking, more weight on the rear axle means you can recapture more energy during deceleration. But it also changes the traction limits—how much force the tires can transmit before slipping. If the battery placement makes the vehicle more likely to spin during aggressive regeneration, the control system must limit how hard it can brake, which reduces efficiency.

These interactions mean that a placement decision isn't just about finding room for components. It's about understanding how spatial choices reshape the physics of the entire system.

The researchers built a framework that makes these couplings explicit. The framework has three main components that work together: a spatial packaging optimizer, a powertrain optimization model, and a battery-structural integration model. These are connected through a coordination strategy called Analytical Target Cascading (ATC), which allows the subproblems to share information while maintaining the specialized mathematics each domain requires.

The spatial packaging optimizer uses a mathematical representation where each component is approximated as a collection of spheres—what the researchers call a Maximal Disjoint Ball Decomposition, or MDBD. This representation has a crucial advantage: checking whether two sphere-based objects collide is computationally simple. The distance between their centers minus their radii tells you immediately whether they overlap. By contrast, representing components with their true geometric shapes—complex CAD surfaces and curved panels—makes collision detection far more expensive and numerically fragile.

The researchers made several methodological improvements to the MDBD approach that are worth understanding in detail.

First, they replaced the traditional way of describing how objects rotate in space. Previous implementations used Euler angles—roll, pitch, and yaw—which are intuitive but suffer from a mathematical singularity called gimbal lock. When two rotation axes align during optimization, the representation collapses, and the solver can no longer determine which direction to move. The researchers switched to quaternion-based rotation, which provides a globally smooth representation without singularities. Every possible orientation of a rigid body corresponds to a unique point in a four-dimensional space, and the optimization can navigate that space without hitting dead ends.

Second, they added a mathematically sophisticated way to enforce that components stay inside the vehicle's available packaging volume. Previous approaches often used penalty functions, which add a cost to the objective when components approach the boundary. But penalty functions create difficult optimization landscapes—many local minima, poor gradients, unpredictable convergence. The researchers instead pre-compute a Signed Distance Field (SDF) across the entire vehicle interior volume. This field assigns every point a positive value if it's inside the admissible space, negative if it's outside, and zero at the boundary. By interpolating this field with cubic B-splines, they obtain a continuously differentiable function that can be used as a hard constraint: components must stay at points where the SDF is greater than zero. The optimization can't violate this constraint—it must find a solution that satisfies it everywhere.

Third, they incorporated alignment constraints for component ports. In a vehicle drivetrain, mechanical connections must leave and enter components in specific directions. An axle that connects a motor to a differential must exit the motor housing at an angle that aligns with the differential input. These directional requirements are now explicit constraints in the optimization, ensuring that solutions are not just collision-free but actually manufacturable.

The powertrain optimization model captures the dependencies between component sizing and vehicle dynamics. It includes models for electric motor efficiency across different operating points, battery discharge characteristics, transmission efficiency, and vehicle longitudinal dynamics. Critically, it receives mass and mass distribution information from the spatial packaging optimizer as inputs, allowing it to compute how placement affects powertrain performance.

The battery-structural integration model captures a modern design approach where the battery pack is not just cargo but a load-bearing structural element. The researchers used a reduced-order analytical model that captures how battery placement affects structural stiffness and mass. Placing the battery lower in the floor improves the vehicle's bending and torsional rigidity, which affects ride quality and handling. This structural benefit must be weighed against packaging constraints and other performance targets.

The coordination strategy—Analytical Target Cascading—handles the communication between these subproblems. In ATC, each subproblem has its own optimization objective, but is also subject to consistency constraints that enforce agreement with shared variables. When the spatial packaging optimizer places components, it proposes values for mass and mass distribution. The powertrain optimizer uses those values to compute performance metrics. If the powertrain optimizer's decisions change the mass significantly—perhaps a larger motor is needed—those changes must propagate back to the spatial model. ATC manages this back-and-forth by coordinating through shared variables while allowing each subproblem to use the mathematical tools best suited to its domain.

The researchers validated their approach using a multi-objective optimization framework based on NSGA-II—the Nondominated Sorting Genetic Algorithm II. Multi-objective optimization is necessary because automotive design inherently involves trade-offs. A design might minimize energy consumption but increase cost, or maximize performance but reduce range. NSGA-II doesn't return a single "best" solution but instead explores the Pareto front: the set of designs where improving one objective necessarily worsens another. This gives engineers a menu of options rather than a single answer.

The test problem combined a complete electric drivetrain with battery chassis integration, representing a realistic automotive design challenge. The drivetrain included multiple electric motors with configurable torque distribution, a single-speed transmission, and a battery system whose mass and spatial position were design variables. The goal was to explore the trade-offs between energy consumption, vehicle performance (acceleration and handling), and structural characteristics.

The researchers implemented their framework in Python, using IPOPT—a widely-used interior point optimizer—for the gradient-based spatial optimization subproblems. The ATC coordination and NSGA-II evolutionary optimization were implemented around this core. The entire framework is modular, meaning the spatial representation, powertrain models, and structural models can be replaced or extended without rewriting the coordination logic.

What They Found

The core finding of this research is not a single number or a single design solution. It is the demonstration that the coupled design space—where component placement, component sizing, and system performance are optimized simultaneously—is qualitatively different from the sequential design space explored by traditional approaches.

In their validation studies, the researchers measured how their quaternion-based spatial optimization approach compared to the traditional Euler-angle representation. The difference was substantial. When testing both methods across a range of random initialization points for the same placement problem, the quaternion method converged to feasible solutions approximately 93 percent of the time. The Euler method converged only about 74 percent of the time. Moreover, among the solutions both methods found, the quaternion approach produced better-quality results: solutions within 10 percent of the best solution found across all trials occurred in 98 percent of quaternion runs, compared to 86 percent for Euler angles.

Convergence Rate Comparison: Quaternion vs Euler Rotation Parameterization

Label	Value
Quaternion Rotation	93
Euler Angles	74

Higher convergence rates indicate more reliable optimization across varying initial conditions

These numbers quantify what the researchers suspected from mathematical reasoning: the Euler representation's singularities create regions of the design space where the optimization cannot make progress, regardless of how clever the algorithm is. The quaternion representation eliminates those dead zones entirely. Engineers using the traditional approach might run the optimization dozens of times from different starting points, hoping that one of them lands in a navigable region. The quaternion approach removes that uncertainty.

More importantly, the research demonstrates that the coupled optimization finds solutions that sequential optimization cannot reach. When component placement is fixed, the powertrain optimizer can only choose among sizes, gear ratios, and control strategies that work with the assumed geometry. When placement is a free variable, the optimizer can discover that a slightly smaller battery placed lower in the vehicle floor produces better overall results than the nominally optimal larger battery in its default position—the mass reduction and center-of-gravity shift outweigh the reduced capacity.

Solution Quality: Solutions Achieving Near-Optimal Results

Label	Value
Quaternion Rotation	98
Euler Angles	86

Percentage of solutions within 10% of the best-known solution across all trials

The framework also outperformed exhaustive search on comparable problems. An exhaustive search discretizes the design space into a grid and evaluates every combination of discrete choices. For a problem with ten components, each with 20 possible positions, that would mean evaluating 20^10—or 10^13—configurations, which is computationally infeasible. The researchers showed that their optimization approach finds better solutions than discretized exhaustive search while requiring far less computation. The optimization is not blindly enumerating options; it is using gradient information and decomposition to navigate the continuous design space intelligently.

Computational Efficiency: SPI2 Framework vs. Exhaustive Search

Label	Value
Discretized Exhaustive Search	100
SPI2 Optimization Framework	65

Relative computational cost comparison for equivalent design space coverage

These results validate the core methodology and demonstrate that the investments in numerical robustness—quaternion rotations, SDF-based constraints, and coordination strategies—pay off in practice.

Why This Changes Things

The automotive industry is in the middle of a fundamental transformation. Electric vehicles eliminate the constraint that the drivetrain must occupy the front of the vehicle, since electric motors can be small enough to fit near wheels or inside wheel hubs. Battery packs that serve as structural elements blur the distinction between energy storage and vehicle architecture. Autonomous driving systems require new sensor configurations that must be integrated into the body design.

These changes mean that vehicle architecture is no longer a solved problem. Engineers are rethinking where components live, how they connect, and what constraints define feasible designs. But the tools they use to explore this new design space are largely inherited from a previous era, when architecture was more constrained and the sequential approach was adequate.

The research from Eindhoven demonstrates what is possible when you build tools that reflect the physics of the actual problem. By treating placement as an explicit optimization variable, by ensuring that the spatial model can communicate with performance models, and by using numerically robust mathematical representations, the framework enables systematic exploration of a design space that has been largely inaccessible.

The implications extend beyond the specific technical results. This work establishes a methodology: a way of thinking about joint optimization of placement and performance that could be adapted to other domains. Electric aircraft face similar challenges—where do you put batteries that must be accessible for maintenance but also positioned to maintain the aircraft's center of gravity? Industrial robots face similar challenges—how do motor placement and gearbox sizing interact? Marine vessels face similar challenges—how do you balance weight distribution with structural requirements?

The framework is also notable for what it does not require. It does not require massive computational infrastructure. The spatial optimization subproblem runs fast enough to be called repeatedly during evolutionary optimization, and the decomposition strategy means that each subproblem only needs to understand its own domain. This modularity makes the approach potentially practical for industrial adoption, since companies do not need to replace their entire design process—they need to implement the coordination strategy and integrate their existing models.

There are, of course, limitations. The MDBD sphere-based representation is an approximation that trades geometric accuracy for computational efficiency. Complex component shapes may not be well-represented by sphere collections, which could affect the quality of placement solutions for components with tight geometric constraints. The powertrain models used for validation are analytical reductions that capture the major physics but not every detail. Real-world manufacturing constraints—weld access, service clearances, thermal expansion—are not yet included.

These limitations are not fatal to the approach. They define areas for future work: improved geometric representations, more detailed physical models, tighter integration with manufacturing constraints. The methodology is sound; the implementation can be extended.

What's Next

The researchers identify several directions for extending this work. The most immediate is tighter integration with detailed CAD models and manufacturing constraints. The current framework operates in a geometric abstraction; real engineering requires accounting for fastener locations, wiring harness routing, thermal expansion, and dozens of other details that are not yet modeled.

Another direction is exploring more complex vehicle architectures. The validation studies focused on a specific drivetrain topology. Modern vehicles might use in-wheel motors, multiple battery packs, or active suspension systems that change the spatial relationships between components dynamically. The framework's modular structure should accommodate these extensions, but testing is needed.

A more ambitious direction is expanding the problem decomposition to handle even larger design spaces. The current ATC coordination manages three subproblems (spatial, powertrain, structural) plus the multi-objective optimizer. Larger systems might require hierarchical decompositions where subproblems are themselves decomposed, introducing additional coordination overhead and new challenges in maintaining solution quality.

The researchers also note opportunities in solution exploration interfaces. Multi-objective optimization produces Pareto fronts with potentially hundreds of non-dominated solutions. Engineers need effective ways to visualize these trade-offs, understand the relationships between design variables and outcomes, and identify solutions that satisfy constraints not captured in the formal optimization model. Visualization and decision support are not solved problems.

Perhaps most fundamentally, this work opens questions about how optimization frameworks should be structured when design spaces are coupled in non-obvious ways. The automotive industry has developed sophisticated tools for individual domains over decades. Integrating those tools into a unified framework requires not just technical coordination but organizational coordination—shared objectives, common data standards, and trust that optimization will produce designs that are actually manufacturable.

The researchers have demonstrated that the technical foundations are sound. The next challenge is integration: making these tools practical for the speed and complexity of modern vehicle development.

For engineers designing the next generation of electric vehicles, the message is clear. Where you put things matters—not just for packaging, but for performance, efficiency, and the fundamental trade-offs that define what a vehicle can do. The old sequential approach constrained that trade-off space in ways that are no longer acceptable. The framework developed at Eindhoven offers a path forward: joint optimization that respects the physics, scales to practical problems, and reveals solutions that would otherwise remain hidden.