In the rapidly evolving field of robotics, the design and development of humanoid robots have garnered significant attention due to their potential to perform complex tasks in human-centric environments. A critical aspect of these humanoid robots is their lower limb structure, which serves as the primary load-bearing component during locomotion and dynamic activities. The weight of these structures directly impacts the overall energy efficiency, agility, and performance of humanoid robots. Traditional manufacturing methods often impose limitations on design complexity, leading to suboptimal weight distribution and structural inefficiencies. However, the integration of laser additive manufacturing (LAM) with topology optimization (TO) presents a transformative approach to overcome these challenges. This combination enables the creation of highly efficient, lightweight, and robust leg structures that are tailored to the specific demands of humanoid robots.
Laser additive manufacturing, a layer-by-layer material deposition process, allows for the fabrication of intricate geometries that are difficult or impossible to achieve with conventional techniques like machining or casting. This technology offers numerous advantages, including reduced lead times from CAD model to physical part, superior mechanical properties, high material utilization, and the elimination of tooling requirements. Importantly, LAM decouples design complexity from manufacturing cost, making it economically viable for producing optimized structures. On the other hand, topology optimization is a mathematical method that optimizes material distribution within a predefined design space to meet specific performance objectives, such as maximizing stiffness or minimizing mass. By intelligently allocating material, TO generates innovative designs that often defy traditional engineering intuition. The synergy between LAM and TO is particularly powerful for humanoid robots, as it enables the realization of complex, weight-optimized leg components that enhance overall system performance.
In this study, we focus on the topology optimization of leg structures for a 75 kg-class humanoid robot, leveraging laser additive manufacturing to achieve significant lightweighting breakthroughs. The leg assembly is divided into two main segments: the calf (lower leg) and the thigh (upper leg). Each segment is subjected to distinct optimization strategies based on their functional requirements. For the calf structure, we employ a mass-minimization objective function to reduce weight while maintaining structural integrity under various loading conditions. Conversely, the thigh structure is optimized for stiffness maximization to ensure stability and support during high-load scenarios. Through iterative computational analyses and finite element validation, we aim to develop leg structures that not only achieve over 50% weight reduction but also exhibit improved mechanical performance and reduced stress concentrations. This approach underscores the potential of advanced design and manufacturing techniques in pushing the boundaries of humanoid robot capabilities.
Methodology for Leg Structure Analysis and Optimization
To initiate the topology optimization process, we first simplify the leg structures of the humanoid robot to eliminate non-essential features that could compromise the accuracy and efficiency of finite element analysis (FEA). The original leg designs include numerous details such as mounting holes,减重孔 (lightening holes), and small connectors, which are removed or streamlined to focus on the primary load-bearing elements. For the calf structure, this involves deleting minor holes on the lateral sides and retaining only critical interfaces. Similarly, the thigh structure is simplified by removing螺纹孔 (threaded holes) and减重槽 (lightening slots) while preserving essential bore holes. This simplification ensures high-quality mesh generation and reliable simulation results, forming a solid foundation for subsequent optimization steps.
Next, we define the load cases to accurately simulate the real-world operating conditions of humanoid robots. Given that the robot is designed to weigh 75 kg, we consider extreme loading scenarios to ensure robustness. For the calf structure, which must withstand up to 10 times the gravitational force in the vertical direction, we apply fixed constraints at the bottom to mimic foot-ground contact without slippage. Three distinct load cases are established:
- Load Case 1: Fixed constraints at the bottom, with downward forces of 3750 N applied at each of the two upper holes.
- Load Case 2: Fixed constraints at the bottom, with distributed loads totaling 1500 N on the cylindrical upper section.
- Load Case 3: Fixed constraints at the bottom, with lateral forces of 750 N each on four protrusions on the side.
For the thigh structure, which must support up to 20 times the gravitational load, fixed constraints are set at the central bearing location, and inward forces of 7500 N per hole are applied at the upper and lower ends. These multi-dimensional load cases comprehensively capture the dynamic motions of humanoid robots, enabling precise optimization.
The design regions for topology optimization are carefully delineated to balance design freedom with functional requirements. Non-design areas include regions near fixed constraints, load application points, and critical interfaces to ensure that optimized structures remain manufacturable and assembly-friendly. For the calf, the design region encompasses most of the structure except the areas around the fixed constraints and load points. Similarly, for the thigh, the central bearing and end holes are excluded from optimization. This strategic partitioning allows the algorithm to redistribute material optimally while preserving essential features.
We then perform static strength analysis to assess the baseline performance of the leg structures. The calf material is AlSi10Mg aluminum alloy, with an elastic modulus of 77 GPa and a yield strength of 300 MPa. The thigh material is a high-strength aluminum alloy with an elastic modulus of 70 GPa and a yield strength of 500 MPa. Using FEA, we evaluate the stress distributions under the defined load cases. The results indicate that the original structures have significant low-stress regions, confirming the potential for topology optimization. For instance, in Load Case 1, the calf structure exhibits a maximum stress of approximately 96 MPa, with stress concentrations near the upper holes. In Load Cases 2 and 3, stress concentrations shift to the bottom constraints, with peak stresses of 120 MPa and 105 MPa, respectively. The thigh structure shows a maximum stress of around 108 MPa under its load case, primarily at the support corners. Since all stresses remain below the yield strengths, the structures are deemed suitable for optimization.
To quantify the material properties and optimization parameters, we present the following table:
| Component | Material | Elastic Modulus (GPa) | Yield Strength (MPa) | Optimization Objective |
|---|---|---|---|---|
| Calf | AlSi10Mg | 77 | 300 | Mass Minimization |
| Thigh | High-Strength Aluminum | 70 | 500 | Stiffness Maximization |
The topology optimization process is formulated mathematically to achieve the desired objectives. For the calf structure, the mass minimization problem is defined as:
$$
\min_{x} m(x) = \int_{\Omega} \rho(x) d\Omega
$$
subject to:
$$
\sigma(x) \leq \sigma_{\text{allow}} \quad \text{and} \quad \text{displacement constraints}
$$
where \( m(x) \) is the total mass, \( \rho(x) \) is the material density, \( \Omega \) is the design domain, \( \sigma(x) \) is the von Mises stress, and \( \sigma_{\text{allow}} \) is the allowable stress (100 MPa for a safety factor of 3.0). Additionally, a minimum thickness constraint of 12 mm is imposed to ensure manufacturability.
For the thigh structure, the stiffness maximization is equivalent to minimizing compliance, expressed as:
$$
\min_{x} c(x) = \mathbf{U}^T \mathbf{K} \mathbf{U}
$$
where \( c(x) \) is the compliance, \( \mathbf{U} \) is the displacement vector, and \( \mathbf{K} \) is the global stiffness matrix. The optimization is subject to a volume constraint that targets over 50% weight reduction.
We employ iterative algorithms, such as the Method of Moving Asymptotes (MMA), to solve these optimization problems. The results provide conceptual designs that highlight optimal material layouts and load paths. However, these raw outputs often contain intricate features that require geometric reconstruction for practical application. We use smoothing techniques and manual adjustments to generate manufacturable models, ensuring compatibility with laser additive manufacturing processes.
Topology Optimization Implementation and Results
For the calf structure, the topology optimization is conducted with mass minimization as the primary goal. The non-design regions include the areas around the upper holes, side holes, and bottom constraints, as illustrated in the design domain划分 (partitioning). The optimization setup incorporates the three load cases to simulate diverse motion states of humanoid robots. After multiple iterations, the algorithm generates a material distribution that reduces weight by over 50%. The initial optimized configuration, however, shows stress concentrations in the upper section under Load Case 1, with a peak stress of 321 MPa exceeding the yield strength. To address this, we perform manual adjustments by adding local supports in high-stress regions. The revised design reduces the maximum stress to 250 MPa, well within the allowable limit, while maintaining significant weight savings. The final optimized calf structure features a complex, organic shape that efficiently transfers loads and minimizes material usage, demonstrating the effectiveness of topology optimization for humanoid robots.
The thigh structure optimization focuses on stiffness maximization to enhance load-bearing capacity. The non-design areas are the central bearing region and the end holes, while the remainder is open for material redistribution. The optimization process converges to a configuration that achieves more than 50% weight reduction. Similar to the calf, the raw optimization output is post-processed to eliminate impractical features and smooth the geometry. The reconstructed model is validated through FEA, showing a maximum stress of 241 MPa under the applied load, which is below the material yield strength. This optimized thigh structure not only reduces weight but also improves stiffness, leading to better performance for humanoid robots during dynamic activities such as walking or running.
To illustrate the optimization outcomes, we summarize the key performance metrics in the following table:
| Performance Metric | Original Calf | Optimized Calf | Original Thigh | Optimized Thigh |
|---|---|---|---|---|
| Mass (kg) | Baseline | >50% Reduction | Baseline | >50% Reduction |
| Max Stress (MPa) | 96-120 | 250 | 108 | 241 |
| Stiffness | Baseline | Maintained | Baseline | Improved |
The optimization results underscore the importance of combining topology optimization with laser additive manufacturing for humanoid robots. The complex geometries generated by TO are readily fabricable using LAM, enabling the production of parts that are both lightweight and strong. For instance, the optimized calf structure transitions from a multi-part assembly to a single, integrated component, reducing the number of parts from 11 to 1 and further enhancing structural integrity. This integration aligns with the broader goal of advancing humanoid robot technology through innovative design and manufacturing solutions.
Strength Validation and Discussion
Following topology optimization, we conduct thorough strength validation to ensure that the optimized leg structures meet engineering requirements. For the calf, the initial optimized design exhibits stress concentrations in the upper region under Load Case 1, necessitating manual reinforcement. The addition of local supports effectively mitigates these stress peaks, as confirmed by FEA. The final design maintains a safety margin, with stresses remaining below the yield strength across all load cases. This iterative process of optimization and validation highlights the practical challenges in applying TO to humanoid robot components, where real-world constraints must be balanced with theoretical ideals.
For the thigh structure, the optimized design is validated under its primary load case. The stress distribution shows that material is efficiently utilized, with no critical areas of overstress. The stiffness maximization objective results in a structure that is not only lighter but also more rigid, contributing to improved stability for humanoid robots. The successful validation of both leg segments demonstrates the robustness of our approach, which combines advanced simulation with practical design adjustments.
We further analyze the impact of optimization on the dynamic performance of humanoid robots. The significant weight reduction in the leg structures lowers the moment of inertia, potentially enhancing agility and reducing energy consumption during locomotion. This is crucial for humanoid robots operating in unstructured environments, where rapid movements and balance are essential. Moreover, the use of laser additive manufacturing allows for the incorporation of internal lattice structures or other lightweighting features that could not be achieved with traditional methods. These advancements pave the way for next-generation humanoid robots with superior mobility and endurance.
However, challenges remain in fully leveraging topology optimization for humanoid robots. The sensitivity of optimized designs to load variations and manufacturing tolerances requires careful consideration. Future work could involve multi-disciplinary optimization, incorporating factors such as thermal management, vibration damping, and impact resistance. Additionally, the integration of machine learning algorithms could accelerate the optimization process and explore broader design spaces for humanoid robots.
Conclusion
In this study, we have demonstrated the successful application of topology optimization and laser additive manufacturing to design lightweight and high-performance leg structures for humanoid robots. By dividing the leg assembly into calf and thigh segments and applying tailored optimization strategies, we achieved over 50% weight reduction while maintaining structural integrity. The calf structure, optimized for mass minimization, required manual adjustments to eliminate stress concentrations, resulting in a design that balances lightweighting and strength. The thigh structure, optimized for stiffness maximization, exhibited improved load-bearing capacity and reduced weight. Both optimized designs were validated through finite element analysis, confirming their suitability for real-world applications.
The synergy between topology optimization and laser additive manufacturing offers a powerful framework for advancing humanoid robot technology. It enables the creation of complex, efficient structures that enhance overall system performance. As research in this field progresses, we anticipate further innovations in design methodologies and manufacturing techniques, ultimately leading to more capable and efficient humanoid robots. This work contributes to the ongoing efforts to push the boundaries of robotics, highlighting the transformative potential of integrated design and manufacturing approaches.