We present an algorithm to compute planar linkage topology and geometry, given a user-specified end-effector trajectory. Planar linkage structures convert rotational or prismatic motions of a single actuator into an arbitrarily complex periodic motion, \refined{which is an important component when building low-cost, modular robots, mechanical toys, and foldable structures in our daily lives (chairs, bikes, and shelves). The design of such structures require trial and error even for experienced engineers. Our research provides semi-automatic methods for exploring novel designs given high-level specifications and constraints.} We formulate this problem as a non-smooth numerical optimization with quadratic objective functions and non-convex quadratic constraints involving mixed-integer decision variables (MIQCQP). We propose and compare three approximate algorithms to solve this problem: mixed-integer conic-programming (MICP), mixed-integer nonlinear programming (MINLP), and simulated annealing (SA). We evaluated these algorithms searching for planar linkages involving $10-14$ rigid links. Our results show that the best performance can be achieved by combining MICP and MINLP, leading to a hybrid algorithm capable of finding the planar linkages within a couple of hours on a desktop machine, which significantly outperforms the SA baseline in terms of optimality. We highlight the effectiveness of our optimized planar linkages by using them as legs of a walking robot.
翻译:我们提出一种算法来计算计划联系的地形学和几何,并给出了一个用户指定的终端效应轨迹。 计划联系结构将单一动因的旋转或扭曲动作转换成一个任意复杂的周期性运动,\ refined{这是建立低成本、模块化机器人、机械玩具和我们日常生活中的折叠结构(椅子、自行车和架子)的重要组成部分。 这种结构的设计需要试验和错误,即使是有经验的工程师也是如此。 我们的研究提供了半自动的方法来探索具有高水平规格和限制的新型设计。 } 我们把这个问题设计成一个非模版数字优化,带有四边形目标功能和非对等的二次等式限制,涉及混合整数决定变量(MIQQQP)。 我们提出并比较了三种大致的算法来解决这个问题:混合内插图、混合内拼图(MIC-Programming)(MICP)、混合整形非线性非线性编程编程(MINLP)和模拟内嵌化(SA)。 我们评估了这些算法,以10-14美元的硬链接来搜索计划,其中含有10-14美元硬性的数字联系。 MICQL 将一个最精确的模型连接。 我们的结果显示MICal 的机的模型在最接近中可以找到一个最精确的MINAL 。