As a parametric motion representation, B\'ezier curves have significant applications in polynomial trajectory optimization for safe and smooth motion planning of various robotic systems, including flying drones, autonomous vehicles, and robotic manipulators. An essential component of B\'ezier curve optimization is the optimization objective, as it significantly influences the resulting robot motion. Standard physical optimization objectives, such as minimizing total velocity, acceleration, jerk, and snap, are known to yield quadratic optimization of B\'ezier curve control points. In this paper, we present a unifying graph-theoretic perspective for defining and understanding B\'ezier curve optimization objectives using a consensus distance of B\'ezier control points derived based on their interaction graph Laplacian. In addition to demonstrating how standard physical optimization objectives define a consensus distance between B\'ezier control points, we also introduce geometric and statistical optimization objectives as alternative consensus distances, constructed using finite differencing and differential variance. To compare these optimization objectives, we apply B\'ezier curve optimization over convex polygonal safe corridors that are automatically constructed around a maximal-clearance minimal-length reference path. We provide an explicit analytical formulation for quadratic optimization of B\'ezier curves using B\'ezier matrix operations. We conclude that the norm and variance of the finite differences of B\'ezier control points lead to simpler and more intuitive interaction graphs and optimization objectives compared to B\'ezier derivative norms, despite having similar robot motion profiles.

Safe corridor-based Trajectory Optimization (TO) presents an appealing approach for collision-free path planning of autonomous robots, offering global optimality through its convex formulation. The safe corridor is constructed based on the perceived map, however, the non-ideal perception induces uncertainty, which is rarely considered in trajectory generation. In this paper, we propose Distributionally Robust Safe Corridor Constraints (DRSCCs) to consider the uncertainty of the safe corridor. Then, we integrate DRSCCs into the trajectory optimization framework using Bernstein basis polynomials. Theoretically, we rigorously prove that the trajectory optimization problem incorporating DRSCCs is equivalent to a computationally efficient, convex quadratic program. Compared to the nominal TO, our method enhances navigation safety by significantly reducing the infeasible motions in presence of uncertainty. Moreover, the proposed approach is validated through two robotic applications, a micro Unmanned Aerial Vehicle (UAV) and a quadruped robot Unitree A1.

There are many industrial, commercial and social applications for multi-agent planning for multirotors such as autonomous agriculture, infrastructure inspection and search and rescue. Thus, improving on the state-of-the-art of multi-agent planning to make it a viable real-world solution is of great benefit. In this work, we propose a new method for multi-agent planning in a static environment that improves our previous work by making it fully online as well as robust to communication latency. The proposed framework generates a global path and a Safe Corridor to avoid static obstacles in an online fashion (generated offline in our previous work). It then generates a time-aware Safe Corridor which takes into account the future positions of other agents to avoid intra-agent collisions. The time-aware Safe Corridor is given with a local reference trajectory to an MIQP (Mixed-Integer Quadratic Problem)/MPC (Model Predictive Control) solver that outputs a safe and optimal trajectory. The planning frequency is adapted to account for communication delays. The proposed method is fully online, real-time, decentralized, and synchronous. It is compared to 3 recent state-of-the-art methods in simulations. It outperforms all methods in robustness and safety as well as flight time. It also outperforms the only other state-of-the-art latency robust method in computation time.

This article presents a multi-robot trajectory planning method which not only guarantees optimization feasibility and but also resolves deadlocks in obstacle-dense environments. The method is proposed via formulating a recursive optimization problem, where a novel safe corridor is generated online to ensure obstacle avoidance in trajectory planning. A dynamic-priority mechanism is combined with the right-hand rule to handle potential deadlocks that are much harder to resolve due to static obstacles. Comparisons with other state-of-the-art results are conducted to validate the improved safety and success rate. Additional hardware experiments are carried out with up to eight nano-quadrotors in various cluttered scenarios.

In the 36th week of war in Ukraine, Russia backed out of a United Nations-sponsored agreement guaranteeing the safe passage of grain ships through the Black Sea, only to rejoin it three days later. Moscow's withdrawal over the weekend renewed fears of a global food crisis – concerns that have not been completely quelled since it rejoined because its return came with conditions. President Vladimir Putin said he reserved the right to back out again if Kyiv used the humanitarian corridor for attacks, the reason Russia gave for the initial pullout. The Kremlin has also warned that it has not yet decided whether to extend the grain deal, which expires in two weeks. Officials in Moscow had said that grain ships may have acted as a cloak for an attack on its naval base on Saturday at Sevastopol on the Crimean Peninsula.

In this paper, we propose a new method for multirotor planning in dynamic environments. The environment is represented as a temporal occupancy grid which gives the current as well as the future/predicted state of all the obstacles. The method builds on previous works in Safe Corridor generation and multirotor planning to avoid moving and static obstacles. It first generates a global path to the goal that doesn't take into account the dynamic aspect of the environment. We then use temporal Safe Corridors to generate safe spaces that the robot can be in at discrete instants in the future. Finally we use the temporal Safe Corridors in an optimization formulation that accounts for the multirotor dynamics as well as all the obstacles to generate the trajectory that will be executed by the multirotor's controller. We show the performance of our method in simulations.

In this paper, we propose a new framework for multi-agent collaborative exploration of unknown environments. The proposed method combines state-of-the-art algorithms in mapping, safe corridor generation and multi-agent planning. It first takes a volume that we want to explore, then proceeds to give the multiple agents different goals in order to explore a voxel grid of that volume. The exploration ends when all voxels are discovered as free or occupied, or there is no path found for the remaining undiscovered voxels. The state-of-the-art planning algorithm uses time-aware Safe Corridors to guarantee intra-agent collision safety as well safety from static obstacles. The presented approach is tested in a state of the art simulator for up to 4 agents.

Safe Corridors (a series of overlapping convex shapes) have been used recently in multiple state-of-the-art motion planning methods. They allow to represent the free space in the environment in an efficient way for collision avoidance. In this paper, we propose a new framework for generating Safe Corridors. We assume that we have a voxel grid representation of the environment. The proposed framework improves on a previous state-of-the-art voxel grid based Safe Corridor generation method. It also creates a connectivity graph between polyhedra of a given Safe Corridor that allows to know which polyhedra intersect with each other. The connectivity graph can be used in planning methods to reduce computation time. The method is compared to other state-of-the-art methods in simulations in terms of computation time, volume covered, safety, number of polyhedron per Safe Corridor and number of constraints per polyhedron.