Achieving numerical accuracy levels for data-driven inverse kinematics
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Inverse Kinematics (IK) is a fundamental challenge in robotic manipulation. It refers to the process of finding the required joint configurations to reach a target end-effector pose. Since this mapping is not uniquely defined, it may yield an infinite number of solutions. Furthermore, deriving a closed-form solution for complex robot configuration, especially those with a high number of Degrees of Freedom (DoF) is often difficult or even impossible. Over the years, several IK methods have been proposed, each with their own strengths and weaknesses. Among these methods, Numerical IK (NIK) solvers are widely recognized as reliable, iterative methods that can achieve state-of-the-art pose accuracies (e.g., low position and orientation errors). However, their performance is highly affected by a range of user-defined parameters. More recently, Data-Driven IK (DDIK) solvers have gained increasing interest in the robotics community. Once their training has been achieved to a significant level of accuracy, DDIK solvers can compute IK solutions more quickly and efficiently than NIK methods (e.g., without an iterative process). However, they are still unable to provide the same level of pose accuracy as NIK methods. This research aims to address the consistency issues encountered with NIK solvers and show that DDIK solvers can achieve the same level of accuracy as NIK solvers. With respect to NIK solvers, our primary motivation is to highlight an issue that has been overlooked by the research community: the necessity of ensuring algorithmic robustness concerning various consistency requirements. This is crucial to avoid undesirable robotic system behaviors. In this regard, we extend our previously proposed approach based on Mixed Generalized Inverse (MX-GI), which builds on the Denhavit-Hartenberg (D-H) methodology, by studying eight (8) well-established inverse Jacobian methods employed in NIK solvers and showing that by using our MX-GI-based approach, as opposed to using other GIs, one can achieve 100 percent identical paths, hence ensuring unit consistency, across all unit choices. We also review six (6) Pseudo-inverse-based Path Planning (PP) schemes from the literature, and show once again that by integrating the MX-GI into these schemes, one can guarantee 100 percent identical path tracking behaviors across all unit choices both in the presence and absence of various noise types. Our experimental results confirm that the MXGI not only ensures consistent system behaviors regardless of unit choices, but also attains comparable accuracy levels. In essence, we demonstrate that "mixing is all you need" for IK and PP of robotic manipulators. With respect to DDIK solvers, our primary motivation is to show that DDIK solvers can achieve the same level of accuracy as NIK solvers. In this regard, we propose a new Learning-By-Example (LBE) strategy where the network input incorporates the previous joint-pose pair and the query pose to predict the desired joint configuration. We evaluated this strategy in a one-to-one IK solution setting under both one-solver-one-robot and one-solver-many-robots frameworks. Our experimental results show that the resulting LBE-DDIK solvers can predict IK solutions with accuracy better than 1mm in position and 1deg in orientation.
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Ph. D.