Differentiable Collision Avoidance Using Collision Primitives

A central aspect of robotic motion planning is collision avoidance, where a multitude of different approaches are currently in use. Optimization-based motion planning is one method, that often heavily relies on distance computations between robots and obstacles. These computations can easily become a bottleneck, as they do not scale well with the complexity of the robots or the environment. To improve performance, many different methods suggested to use collision primitives, i. e. simple shapes that approximate the more complex rigid bodies, and that are simpler to compute distances to and from. However, each pair of primitives requires its own specialized code, and certain pairs are known to suffer from numerical issues. In this paper, we propose an easy-to-use, unified treatment of a wide variety of primitives. We formulate distance computation as a minimization problem, which we solve iteratively. We show how to take derivatives of this minimization problem, allowing it to be seamlessly integrated into a trajectory optimization method. We demonstrate that the resulting method can be used to plan smooth and collision-free paths based on a variety of single- and multi-robot scenarios with different obstacles.

Authors

• Simon Zimmermann
• Matthias Busenhart
• Simon Huber
• Roi Poranne
• Stelian Coros

Keywords

• Robot motion
• Codes
• Shape
• Minimization
• Planning
• Complexity theory
• Collision avoidance
• Rigid Body
• Path Planning
• Distance Calculation
• Trajectory Optimization
• Numerous Issues
• Simple Shapes
• Collision-free Path
• Optimization Problem
• Computation Time
• Inequality Constraints
• Shortest Distance
• Regularization Term
• Newton Method
• Joint Angles
• Robotic Arm
• Gradient-based Methods
• Hausdorff Distance
• Soft Constraints
• Multiple Robots
• Empty Box
• Collision-free Trajectory
• Trajectory Optimization Problem
• Cluttered Environments
• World Coordinate
• Sensitivity Matrix
• Physical Robot
• Signed Distance Function
• Ellipsoid
• Distance Function
• Distance Map