ContinuousTime Collision Avoidance for Trajectory Optimization in Dynamic Environments Common formulations to consider collision avoidance in trajectory optimization often use either preprocessed environments or only check and penalize collisions at discrete time steps. However, when only checking at discrete states, this requires either large margins that prevent manipulation close to obstacles or dense time discretization increasing the dimensionality of the optimization problem in complex environments. Nonetheless, collisions may still occur in the interpolationtransition between two valid states or in environments with thin obstacles. In this work, we introduce a computationally inexpensive continuoustime collision avoidance term in presence of static and moving obstacles. Our penalty is based on conservative advancement and harmonic potential fields and can be used as either a cost or constraint in offtheshelf nonlinear programming solvers. Due to the use of conservative advancement (collision checks) rather than distance computations, our method outperforms discrete collision avoidance based on signed distance constraints resulting in smooth motions with continuoustime safety while planning in discrete time. We evaluate our proposed continuous collision avoidance on scenarios including manipulation of moving targets, locomanipulation on mobile robots, manipulation trajectories for humanoids, and quadrotor path planning and compare penalty terms based on harmonic potential fields with ones derived from contact normals.

Rapid Collision Detection for Multicopter Trajectories We present a continuoustime collision detection algorithm for quickly detecting whether certain polynomial trajectories in time intersect with convex obstacles. The algorithm is used in conjunction with an existing multicopter trajectory generation method to achieve rapid, obstacleaware motion planning in environments with both static convex obstacles and dynamic convex obstacles whose boundaries do not rotate. In general, this problem is difficult because the presence of convex obstacles makes the feasible space of trajectories nonconvex. The performance of the algorithm is benchmarked using Monte Carlo simulations, and experimental results are presented that demonstrate the use of the method to plan collisionfree multicopter trajectories in milliseconds in environments with both static and dynamic obstacles.