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Systematic Lightweight Method for Robotics Based on Strain Energy Distribution Optimization
Jingchen Li
TL;DR
Complex service robots need lightweight designs, but optimizing many components across varied configurations and loads creates a difficult system-level problem. The paper introduces strain-energy-distribution optimization, using uniform specific strain energy to assign part objectives and enable separate optimization with different methods. The method retains system-level optimization while reducing computational complexity to the part level and is demonstrated across robotic-arm design cases.
Problem
Complex robots require lightweight, safe, energy-efficient designs across many components, configurations, and load environments, making effective system-level optimization challenging.
Method
The method uses uniformly distributed strain energy per unit mass to decouple system optimization into part-level problems with separately assigned objectives.
Results
The method retains systematic optimization while reducing computational complexity to the part level and supports different optimization methods for individual parts.
Takeaways & Limitations
The approach provides a flexible systematic framework for lightweight optimization of complex mechanical systems while avoiding system-level computational complexity.
Takeaways & Limitations
The criterion is formally proven only for serial-chain systems; for more complex topologies, support comes from finite-element validation rather than formal proof.
Abstract
from arXiv · showhide
Service robots work with people and are highly expected to be lightweight for safety, agility and energy conservation. As a complex mechanical system, a robot consists of a large number of components and has various working configurations and load environments. An effective method for achieving system-level optimal robot design is a crucial requirement, but it poses significant challenges. In this study, we introduce a novel approach to optimize the distribution of strain energy, which can significantly improve the effectiveness of systematic optimization in a complex system. First, we present and demonstrate that the strain energy per unit mass should be uniformly distributed in an optimal lightweight mechanical system. Based on this criterion, the system-level problem can be decoupled and the design objective of each part can be assigned based on the strain energy. Then, each part can be optimally designed separately according to its specific circumstances by using different approaches, such as size optimization, topological optimization, and material optimization. In this way, the optimization is at the system level, while the computational complexity is at the part level. Weight reduction and improvements in mechanical properties can be obtained simultaneously. As an example, this method is applied to an arbitrarily designed robotic arm, and its effectiveness is further demonstrated in the cases of lightweight with stiffness improvement, considering multiple materials, multiple working conditions, and vibration performance.
1 Introduction
Service robots require lightweight, compact mechanical systems for safe, dexterous, energy-efficient operation, but their many components and working conditions make system-level optimization difficult. Existing lightweight methods often target individual parts, motivating a systematic approach that decouples the robot into part-level optimization problems.
- Motivation: Service robots need lightweight, compact designs for safe dexterity and reduced battery power consumption.Their complex tasks, configurations, and force environments make lightweight design especially challenging.
- Motivation: Mechanical structures and actuators contribute significantly to robot weight, with actuator lightweighting commonly pursued through improved power density and compact integration.
- Existing Lightweight Design: Structures must balance strength and deformation against weight, motivating topology optimization, additive manufacturing, lattice structures, and composite materials.These approaches can improve mechanical properties while reducing mass.
- System-Level Challenge: Optimizing robot parts independently for maximum stiffness-to-mass ratio does not necessarily maximize stiffness at the system level.Because parts collectively determine system properties, systematic optimization is necessary.
- System-Level Challenge: Whole-assembly topology optimization is computationally expensive, while size optimization is less effective and difficult to parameterize for complex robotic structures.Synchronous assembly optimization also cannot apply different optimization methods to different parts.
- Proposed Approach: The proposed approach decouples system optimization by uniformly distributing specific strain energy and assigning each part an aligned optimization objective.Specific strain energy is used because it incorporates material properties and reflects structural strength and stiffness.
2 Strain Energy Distribution Optimization Method
The method uses specific strain energy—strain energy per unit mass—as a system-level indicator, hypothesizing that it should be uniform in an optimal lightweight design. This criterion enables system optimization to be decoupled into part-level designs with assigned strain-energy targets.
- Strain-energy criterion: Specific strain energy combines material-aware strength and stiffness information into a scalar indicator for comparing different parts.It is defined as strain energy per unit mass.
- Strain-energy criterion: The proposed optimality condition is equal specific strain energy across all parts of the mechanical system.The condition applies to Ui/mi, which is distinct from volumetric strain energy density u.
- Proof and verification: For general series beam systems, mechanics-based analysis shows that the optimal stiffness-to-weight ratio requires equal specific strain energy among parts.The proof covers rods that may undergo tension, compression, torsion, bending, or combined deformation, with the stated slender-rod assumptions.
- Proof and verification: FEA verification with three differently assigned materials shows specific strain energies converge toward equality while total strain energies do not.The examples optimize rod radii under an end-deformation constraint of dend ≤2mm; the standard deviation of specific strain energies approaches zero.
- Systematic optimization: The system-level problem is decoupled by assigning each part an expected strain energy, after which parts can be optimized separately.The framework supports part-level approaches such as size, topology, or material optimization while retaining system-level targets.
- Systematic optimization: Using the mass before optimization is convenient but introduces obvious error because changing part masses prevents final specific strain energy from becoming uniform.The approximation may be reasonable when the initial mass distribution is supplied by an experienced designer.
3 Test and Compare the Methods
The methods are compared on a three-part structure against global topology optimization, showing that strain-energy-based part-level optimization approaches the global reference while reducing computational demands. Iterative and metamodel variants produce similar lightweight designs, but connection modeling leaves a small performance gap.
- Example and reference: 3.54kg with 4.5mm end deformation is obtained by global topological optimization, providing the system-level reference.The global method optimizes minimum weight under the specified deformation constraint.
- Strain-energy-based methods: Strain-energy-based part optimization yields 3.88kg with Method 1 and 3.69kg with Method 2, approaching the global optimum.Method 1 assigns expected strain energy after initial FEA; Method 2 iterates using averaged previous masses and converges by the third step.
- Strain-energy-based methods: Method 2 diverges when the last optimized mass is reused directly, whereas averaging previous masses produces rapid convergence and progressively lighter designs.The convergent iteration reaches 3.69kg and is closer to the global optimization result.
- Strain-energy-based methods: Method 3 also reaches 3.69kg, with nearly identical topologies to Method 2, indicating equivalent results but higher computational cost.Method 3 fits a mass–stiffness metamodel from topology-optimization samples before solving for expected strain energies.
- Limitations and trade-offs: The proposed methods remain slightly heavier because REB3 connection elements underestimate interface stiffness during separate part optimization.This weaker interface modeling strengthens connection regions and creates a small gap from the global optimum.
- Limitations and trade-offs: Global optimization is optimal, whereas Methods 1 and 2 are recommended for computational-cost/error trade-offs and Method 3 is more costly.The authors report that all proposed methods achieve systematic optimization and outperform non-systematic methods.
4 Optimization of Robotic Arm
The robotic-arm example applies strain-energy-based system decomposition across multiple materials and load conditions, then uses part-level material and topology optimization. The resulting designs reduce weight while meeting deformation targets and improving stiffness consistency.
- System setup: The robotic arm is evaluated under five horizontal poses that capture the worst loads on each link, using full-model FEA with a 5 kg end load and gravity.The arm has seven main links and six joint actuators; the actuators are held fixed during optimization.
- Strain-energy allocation: Expected whole-arm and part-level strain energies are calculated for three deformation targets—2 mm, 2.5 mm, and 3 mm—to assign optimization objectives.Parts below their expected strain energy are identified as weak points, while parts above it are treated as redundant.
- Part-level optimization: Material selection and topology optimization are combined at the part level, with material changes used to bring expected and current strain energies closer.The method considers commonly used metallic materials and produces density distributions for the optimized parts.
- Part-level optimization: Less material is retained when the expected-to-current strain-energy ratio is larger, and two rounds of part-level optimization provide an effective system-level design.The optimization uses five simultaneous deformation constraints and REB3 elements to represent part boundaries, connections, and remote forces.
- Results: The structural weight decreases from 7.116 kg to 4.266 kg, 3.298 kg, and 2.824 kg for the 2 mm, 2.5 mm, and 3 mm targets, respectively.Full-model FEA shows that maximum deformations remain below the corresponding targets after assembly.
- Results: The optimized arm maintains target stiffness, reduces differences among load conditions, and improves the isotropy of the system’s mechanical properties.Vibration performance is assessed through modal quantities such as natural frequencies, although it is not directly mapped to strain energy.
5 Conclusions
The paper concludes that uniform specific strain energy can decompose systematic lightweight optimization into flexible part-level problems while retaining system-level objectives. It reports substantial theoretical weight reduction with stiffness control, but identifies manufacturing constraints and limited theoretical generalization as practical boundaries.
- Main contribution: The proposed criterion uniformly distributes specific strain energy across a system at the optimal stiffness-to-weight ratio, enabling system-level optimization through part-level problems.The approach can use different part-level methods while avoiding system-level computational complexity.
- Main contribution: The method achieves weight reduction together with stiffness control, improvement, or maintenance, while remaining more flexible and less computationally costly than the metamodel approach.The conclusion presents the robotic-arm example as evidence under multiple loads, materials, and vibration considerations.
- Practical limitations: Manufacturing methods, costs, appearance, and added redesign weight can reduce the lightweight effect, making preservation of theoretical savings during manufacturing an open problem.The paper identifies direct 3D printing as an ideal way to preserve the lightweight effect, while manufacturing constraints reduce it to some extent.
- Theoretical limitation: The uniform-specific-strain-energy criterion is formally derived only for serial-chain systems; more complex structural topologies currently rely on FEA validation and require further theoretical investigation.This limits the formal scope of the criterion beyond serial-chain systems.
- Implementation considerations: Only two optimization iterations are used because the second yields a 0.3 kg reduction and a predicted third yields only 0.1–0.2 kg, indicating low cost-to-benefit for further iterations.REB3 elements also weaken modeled connection interfaces and underestimate stiffness relative to direct connections.