Inverse kinematics (IK) is the problem of finding robot joint configurations that satisfy constraints on the position or pose of one or more end-effectors. For robots with redundant degrees of freedom, there is often an infinite, nonconvex set of solutions. The IK problem is further complicated when collision avoidance constraints are imposed by obstacles in the workspace. In general, closed-form expressions yielding feasible configurations do not exist, motivating the use of numerical solution methods. However, these approaches rely on local optimization of nonconvex problems, often requiring an accurate initialization or numerous re-initializations to converge to a valid solution. In this work, we first formulate inverse kinematics with complex workspace constraints as a convex feasibility problem whose low-rank feasible points provide exact IK solutions. We then present \texttt{CIDGIK} (Convex Iteration for Distance-Geometric Inverse Kinematics), an algorithm that solves this feasibility problem with a sequence of semidefinite programs whose objectives are designed to encourage low-rank minimizers. Our problem formulation elegantly unifies the configuration space and workspace constraints of a robot: intrinsic robot geometry and obstacle avoidance are both expressed as simple linear matrix equations and inequalities. Our experimental results for a variety of popular manipulator models demonstrate faster and more accurate convergence than a conventional nonlinear optimization-based approach, especially in environments with many obstacles.
翻译:反动动直线( IK) 是找到机器人联合配置的问题, 以满足对一个或一个以上终端效应的方位或构成构成的制约。 对于具有冗余自由度的机器人来说, 通常会有无限的、 非convex 的一套解决方案。 当工作空间设置障碍, 造成避免碰撞的限制时, IK 问题就更加复杂。 一般来说, 产生可行配置的封闭式表达式不存在, 激励使用数字解答方法。 然而, 这些方法依赖于本地优化非convex问题, 往往需要精确的初始化或无数的重新初始化, 才能凝聚到一个有效的解决方案。 对于具有复杂工作空间限制的机器人, 我们首先设计具有复杂工作空间限制的反动动运动, 是一个配置低级别可行的IK 解决方案。 然后我们介绍 远程地球- Geetoismormalization Explical Explications, 这种算法可以解决这一可行性问题, 其目标旨在鼓励低位最小化的最小化环境。 在这项工作中, 我们的问题是简单化的、 不精确的、 直径直径的模型的模型的模型中, 也是我们所陈式的模型的模型的模型的模型的模型的模型, 。