In the rapidly evolving field of industrial automation and intelligent manufacturing, modular robots have emerged as a pivotal innovation due to their inherent flexibility and adaptability. As a researcher deeply immersed in advancing robot technology, I recognize the critical need for efficient design methodologies that can swiftly generate optimal robot configurations tailored to specific tasks. Traditional approaches often struggle with the immense and nonlinear design space of modular robots, leading to suboptimal solutions. To address this, we propose a performance-driven multi-objective optimization framework that leverages advanced algorithms to explore and identify the best configurations. This article delves into our methodology, emphasizing the integration of continuous design variables and comprehensive performance metrics to enhance robot technology. By focusing on key objectives such as total mass, unit workspace, and global manipulability, our approach ensures that the resulting robot configurations meet diverse operational demands while pushing the boundaries of robot technology innovation.
The foundation of our work lies in the modular design of robots, where standardized components—joint modules and link modules—are combined to form various configurations. This modularity not only simplifies manufacturing and maintenance but also enables rapid reconfiguration for different applications, a hallmark of modern robot technology. However, the challenge arises in selecting the optimal combination of modules and their parameters to achieve desired performance. In this context, we have developed a robust optimization model that incorporates integer coding for design variables, allowing for continuous variation in link dimensions within specified ranges. This innovation addresses a common limitation in prior robot technology studies, where discrete size options restricted the search for optimal solutions. Through extensive simulations and analysis, we demonstrate that our method yields Pareto-optimal configurations with improved dispersion and correlation insights, ultimately advancing the state of robot technology in practical applications.
To begin, let us outline the modular library that forms the basis of our robot technology. We categorize modules into two primary types: joint modules and link modules. Joint modules serve as the actuation units, with five distinct models characterized by parameters such as mass, diameter, output torque, and rated speed. These T-shaped joints facilitate rotational movements and are interconnected via specialized coupling modules to maintain structural integrity. For instance, the coordinate transformation matrix for a joint module, which is essential for kinematic analysis in robot technology, can be expressed as:
$$ {}^a_bT = {}^a_sT \cdot {}^s_bT = \begin{bmatrix} \cos \theta & -\sin \theta & 0 & 0 \\ 0 & 0 & 1 & s_2 \\ -\sin \theta & -\cos \theta & 0 & s_1 \\ 0 & 0 & 0 & 1 \end{bmatrix} $$
where $\theta$ represents the joint angle, and $s_1$, $s_2$ are offsets. Similarly, link modules include cylindrical and corner types, with cylindrical links having a continuous length range of 100–400 mm to enhance design flexibility in robot technology. The transformation matrix for a cylindrical link is given by:
$$ {}^a_bT = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & L \\ 0 & 0 & 0 & 1 \end{bmatrix} $$
where $L$ denotes the link length. These matrices enable rapid derivation of forward kinematics for any modular configuration, a crucial aspect of robot technology that supports real-time control and simulation.
Our optimization model is built upon three key performance objectives that are central to evaluating robot technology: total mass, unit workspace, and global manipulability. The total mass, $f_1$, is the sum of masses from all joint and link modules, as shown in the equation:
$$ f_1 = \sum (M_j + M_l) $$
where $M_j$ and $M_l$ are the masses of joint and link modules, respectively. Minimizing $f_1$ is vital in robot technology to improve the payload-to-weight ratio and energy efficiency. The unit workspace, $f_2$, quantifies the effective operational volume per unit length of the robot, calculated using Monte Carlo methods for workspace volume $V$ and normalized by the total link length:
$$ f_2 = \frac{V}{\sum_{i=1}^n l_i} $$
Here, $V = \int_{z_{\text{min}}}^{z_{\text{max}}} \int_{y_{\text{min}}}^{y_{\text{max}}} \int_{x_{\text{min}}}^{x_{\text{max}}} dx dy dz$ represents the workspace volume, and $l_i$ are the individual link lengths. This metric ensures that robot technology designs maximize spatial coverage without excessive material usage. Lastly, the global manipulability, $f_3$, assesses the robot’s dexterity across its entire workspace, derived from the manipulability measure $\mu = \sqrt{\det(J \cdot J^T)}$, where $J$ is the Jacobian matrix. The global measure is defined as:
$$ f_3 = \frac{\int_w \mu dw}{\int_w dw} $$
where $w$ denotes points in the workspace. A higher $f_3$ indicates better overall motion performance, a key goal in advanced robot technology.
In addition to these objectives, our optimization incorporates several constraints to ensure practicality in robot technology applications. Reachability constraints guarantee that the end-effector can access all task points, expressed as $\| T(q) – T_d \| \leq \varepsilon_p$, where $T(q)$ is the end-effector pose and $T_d$ is the target pose. Joint limits are enforced as $q_{\text{min}} \leq q \leq q_{\text{max}}$, and module sequencing requires that base modules have higher torque capacities than distal ones: $T_{\text{mod}_i} \geq T_{\text{mod}_{i+1}}$. Furthermore, the degree-of-freedom constraint, $n_{\text{min}} \leq n_{\text{dof}} \leq n_{\text{max}}$, allows flexibility in complexity, while connection rules prevent invalid module assemblies, such as direct joint-to-joint linkages that lack functional meaning in robot technology.
To solve this multi-objective optimization problem, we employ the Non-dominated Sorting Genetic Algorithm II (NSGA-II), a popular choice in robot technology for handling complex, nonlinear spaces. The genetic encoding scheme uses integer codes to represent design variables, including joint types, connection directions, link types, and continuous link lengths within [100, 400] mm. This approach enables a dynamic chromosome length that adapts to varying degrees of freedom, enhancing the search capability in robot technology design. The algorithm流程 involves initializing a random population, evaluating fitness based on the three objectives, and applying crossover, mutation, and selection operators to evolve solutions toward the Pareto front. Key parameters for the algorithm are summarized in the table below:
| Parameter | Value |
|---|---|
| Population Size | 100 |
| Maximum Generations | 200 |
| Crossover Probability | 0.8 |
| Stopping Criterion | 5 (generations without improvement) |
We conducted two optimization instances to validate our approach in robot technology: one with discrete link lengths (100, 200, 300, 400 mm) and another with continuous lengths in the same range. For a fair comparison, both instances were constrained to 6 degrees of freedom. The results, illustrated through Pareto fronts, show that the continuous-length instance produced a solution set with reduced dispersion, as measured by the average Euclidean distance between points. Specifically, the discrete instance had an average distance of 435.075, while the continuous instance achieved 499.4398—a 12.89% improvement in concentration. This underscores the advantage of continuous variables in refining robot technology designs.
Further analysis using Pearson correlation coefficients revealed relationships between the optimization objectives. The correlation between unit workspace ($f_2$) and global manipulability ($f_3$) was -0.701, indicating a strong negative interdependence, whereas total mass ($f_1$) and unit workspace ($f_2$) showed negligible correlation (0.007). These insights are crucial for robot technology development, as they highlight trade-offs that designers must consider. For example, enhancing dexterity may come at the cost of workspace efficiency, a common dilemma in robot technology applications.
To illustrate practical implications, we selected two configurations from the Pareto set for simulation in MATLAB. Configuration A had a total mass of 12.12 kg, unit workspace of 3.0173, and global manipulability of 1013.8, while Configuration B shared the same mass but exhibited a unit workspace of 3.4624 and global manipulability of 963.32. Workspace simulations with 20,000 random points demonstrated that Configuration A sacrificed 12.86% in unit workspace compared to Configuration B but gained 5.24% in global manipulability. This trade-off exemplifies the nuanced decision-making required in robot technology, where optimal configurations depend on specific task priorities.
In conclusion, our multi-objective optimization framework significantly advances robot technology by enabling the efficient design of modular robot configurations. The use of continuous design variables and comprehensive performance metrics ensures that Pareto-optimal solutions are both diverse and high-performing. Through correlation analysis and simulations, we have validated the method’s effectiveness in balancing competing objectives, such as workspace coverage and manipulability. Future work in robot technology could focus on developing user-friendly selection strategies from the Pareto set, making this approach accessible to non-experts. As robot technology continues to evolve, such optimization techniques will play a pivotal role in creating adaptable, high-performance robots for a wide range of industrial and service applications, ultimately driving innovation in the field.
Throughout this exploration, we have emphasized the importance of integrating advanced algorithms with practical constraints to push the boundaries of robot technology. The continuous evolution of robot technology demands such holistic approaches, and we are confident that our contributions will inspire further research and development. By leveraging these methods, designers can rapidly generate robot configurations that not only meet immediate task requirements but also adapt to future challenges, solidifying the role of robot technology as a cornerstone of modern automation.