Efficient Learning of Fast Inverse Kinematics with Collision Avoidance

TL;DR

The paper addresses the challenge of computing collision-free inverse kinematics for high-DoF robots in arbitrary, sensor-derived environments. It combines an optimization-based IK framework with learning-based warm-starts, offering supervised and unsupervised training paths, and encodes environments with Basis Point Set. The key contributions are a fast solver achieving under 10 ms on a CPU for a 19-DoF humanoid, a twin-headed network with a singularity-free unit-vector output, and an unsupervised training regime that bypasses data generation while delivering comparable or better performance than supervised training. The results show large speedups and robust generalization to unseen 3D scenes, making real-time collision-free IK practical for real-world manipulation and grasping tasks.

Abstract

Fast inverse kinematics (IK) is a central component in robotic motion planning. For complex robots, IK methods are often based on root search and non-linear optimization algorithms. These algorithms can be massively sped up using a neural network to predict a good initial guess, which can then be refined in a few numerical iterations. Besides previous work on learning-based IK, we present a learning approach for the fundamentally more complex problem of IK with collision avoidance. We do this in diverse and previously unseen environments. From a detailed analysis of the IK learning problem, we derive a network and unsupervised learning architecture that removes the need for a sample data generation step. Using the trained network's prediction as an initial guess for a two-stage Jacobian-based solver allows for fast and accurate computation of the collision-free IK. For the humanoid robot, Agile Justin (19 DoF), the collision-free IK is solved in less than 10 milliseconds (on a single CPU core) and with an accuracy of 10^-4 m and 10^-3 rad based on a high-resolution world model generated from the robot's integrated 3D sensor. Our method massively outperforms a random multi-start baseline in a benchmark with the 19 DoF humanoid and challenging 3D environments. It requires ten times less training time than a supervised training method while achieving comparable results.

Figures (9)

• Figure 1: DLR's Agile Justin Bauml2014 in a shelf environment. The frames for the IK problem were sampled randomly in the respective boxes of the shelf (left). On the right, the previous solution was blocked and made infeasible by placing an additional obstacle in the workspace, leading to a different collision-free solution. Details about the training datasets, networks, and videos can be found on the paper's website.
• Figure 2: The three robots used in the experiments in environments generated with Simplex Noise Perlin2001. The Flat Arm in 2D helps to analyze and visualize the IK problem in detail. The LWR III and Agile Justin demonstrate the capabilities of our method for complex robotic systems.
• Figure 3: The graphic shows the flow of information through the neural network. The IK problem is described by a world $x_{\text{w}}$, and a frame in the workspace $x_{\text{f}}$ and the network should predict a collision-free joint configuration that satisfies the end-effector. The dotted line indicates the backpropagation during unsupervised training, where the network weights $\Theta$ are directly updated according to the gradient of the cost function $U$. In the lower half, the detailed network structure for inverse kinematics of Agile Justin (19 Dof) is shown, with two heads and the unit vector representation for the joint angles described in \ref{['sec:Learning-the-Inverse-Kinematics']}.
• Figure 4: Feasibility map (right/blue) for the 2D arm with 5 DoF for a specific environment. Depending on the robot's kinematics, not only the parts of the workspace with obstacles are unreachable, but also areas behind obstacles. The overall number of feasible poses decreases towards the borders of the workspace. The maximal position error (center/green) and the maximal orientation error (left/red) highlight which regions are challenging for the network in more detail. The error maps show the maximal error over all orientations for each 2D position in the image.
• Figure 5: In the left image, 50 random but feasible samples for the robot in the given environment are drawn in red, and in blue, 50 samples that were in the hard set after the training finished (see \ref{['sec:Boosting']}). The challenging samples are more extended and fill the narrow passages in the world better than the random samples. In the right image, the predictions of the twin heads for a random sample are shown. While satisfying the end-effector, the two configurations show two distinct modes.