Waveform based Inverse Kinematics Algorithm of Kinematically Redundant 3-DOF Manipulator

This paper presents a new approach to the problem of inverse kinematics by modelling robot arm movements as signals generated from algebra-based solutions. The inverse kinematics of point P(xP,yP) are modelled as sinusoidal functions with mechanical constraints. Unique wave forms occur at each point in the workspace. There are four types of inverse kinematic waves depending on how sinusoidal waves cross the value of mechanical constraints. In terms of tracking the path, the robot's arm produces complex waves that produce the desired movement. Due to mechanical constraints, many points in the workspace have the bandwidth where the signal is produced only at limited intervals from the angular domain. Tracks must be stored at these appropriate intervals, which build bandwidth tunnels, completely from the initial configuration to the final configuration. Simulations will be carried out using 3-DOF series planar robots to track highly complex mathematical curves. With a wave-based approach, the solution of the IK problem can benefit from wave characteristics such as the superposition principle

One Network, Many Robots: Generative Graphical Inverse Kinematics

Quickly and reliably finding accurate inverse kinematics (IK) solutions remains a challenging problem for robotic manipulation. Existing numerical solvers are broadly applicable, but rely on local search techniques to manage highly nonconvex objective functions. Recently, learning-based approaches have shown promise as a means to generate fast and accurate IK results; learned solvers can easily be integrated with other learning algorithms in end-to-end systems. However, learning-based methods have an Achilles' heel: each robot of interest requires a specialized model which must be trained from scratch. To address this key shortcoming, we investigate a novel distance-geometric robot representation coupled with a graph structure that allows us to leverage the flexibility of graph neural networks (GNNs). We use this approach to train the first learned generative graphical inverse kinematics (GGIK) solver that is, crucially, "robot-agnostic"-a single model is able to provide IK solutions for a variety of different robots. Additionally, the generative nature of GGIK allows the solver to produce a large number of diverse solutions in parallel with minimal additional computation time, making it appropriate for applications such as sampling-based motion planning. Finally, GGIK can complement local IK solvers by providing reliable initializations. These advantages, as well as the ability to use task-relevant priors and to continuously improve with new data, suggest that GGIK has the potential to be a key component of flexible, learning-based robotic manipulation systems