UC San Diego

Numerous robotics applications, such as path planning, trajectory optimization, and optimal robot placement, involve determining solutions in the robot’s configuration space (C-space), the space of all possible configurations the robot may take. For robot manipulators with many joints, the C-space is high-dimensional with typically nontrivial regions of feasibility, such as the set of collision-free configurations. Creating exact models for these regions of C-space becomes unwieldy for even simple robot manipulators. Without a model of the robot’s C-space, the most popular approaches to solving problems in C-space involve randomly sampling hundreds

to thousands of robot configurations, which unfortunately also requires computationally-expensive verification of the validity of each of these samples. To avoid or alleviate the computational burden associated with validity checking, we explore the challenge of accurately and efficiently approximating models for a robot’s C-space in this work.

We propose the Fastron algorithm, a learning-based approach to model a robot’s C-space. This algorithm creates a nonlinear model that identifies whether a query robot configuration is either in-collision or collision-free an order of magnitude faster than state-of-the-art validity checking algorithms. To further improve the accuracy of the Fastron model, we develop a new similarity function called the forward kinematics (FK) kernel. With the new FK kernel, model accuracy increased to 95%, a significant improvement over the 75% accuracy when using the original similarity function. Using the Fastron model with the FK kernel for validity checking enabled up to 3 times faster motion planning solutions. As the FK kernel has the properties of a covariance function, we also apply this kernel to Gaussian process (GP) regression to estimate a robot’s distance to collision. The GP model obtains accurate distance estimates 70-80 times faster and allows an order of magnitude faster convergence for trajectory optimization when compared

to geometric distance evaluation techniques. With each of these contributions, we demonstrate the advantage of learning-based robot configuration space modeling.