From quadrotors delivering packages in urban areas to robot arms moving in confined
warehouses, motion planning around obstacles is a core challenge in modern robotics …

We present a fast algorithm for the design of smooth paths (or trajectories) that are
constrained to lie in a collection of axis-aligned boxes. We consider the case where the …

Many computations in robotics can be dramatically accelerated if the robot configuration
space is described as a collection of simple sets. For example, recently developed motion …

Convex polytopes have compact representations and exhibit convexity, which makes them
suitable for abstracting obstacle-free spaces from various environments. Existing methods …

We present an efficient method for certifying non-collision for piecewise-polynomial motion
plans in algebraic reparametrizations of configuration space. Such motion plans include …

In this work, we propose a trajectory optimization approach for robot navigation in cluttered
3D environments. We represent the robot's geometry as a semialgebraic set defined by …

This work proposes a safety-critical local reactive controller that enables the robot to
navigate in unknown and cluttered environments. In particular, the trajectory tracking task is …

Collision-avoiding motion planning for articulated robotic arms is one of the major
challenges in robotics. The difficulty of the problem arises from its high dimensionality and …

We consider large-scale, implicit-search-based solutions to Shortest Path Problems on
Graphs of Convex Sets (GCS). We propose GCS*, a forward heuristic search algorithm that …

We present a semi-infinite program (SIP) solver for trajectory optimizations of general
articulated robots. These problems are more challenging than standard nonlinear program …