There is extensive literature on using convex optimization to derive piece-wise polynomial trajectories for controlling differential flat systems with applications to three-dimensional flight for Micro Aerial Vehicles. In this work, we propose a method to formulate trajectory generation as a quadratic program (QP) using the concept of a Safe Flight Corridor (SFC). The SFC is a collection of convex overlapping polyhedra that models free space and provides a connected path from the robot to the goal position. We derive an efficient convex decomposition method that builds the SFC from a piece-wise linear skeleton obtained using a fast graph search technique. The SFC provides a set of linear inequality constraints in the QP allowing real-time motion planning. Because the range and field of view of the robot's sensors are limited, we develop a framework of Receding Horizon Planning , which plans trajectories within a finite footprint in the local map, continuously updating the trajectory through a re-planning process. The re-planning process takes between 50 to 300 ms for a large and cluttered map. We show the feasibility of our approach, its completeness and performance, with applications to high-speed flight in both simulated and physical experiments using quadrotors.

Planning Dynamically Feasible Trajectories for Quadrotors Using Safe Flight Corridors in 3-D Complex Environments

The use of aerial swarms to solve real-world problems has been increasing steadily, accompanied by falling prices and improving performance of communication, sensing, and processing hardware. The commoditization of hardware has reduced unit costs, thereby lowering the barriers to entry to the field of aerial swarm robotics. A key enabling technology for swarms is the family of algorithms that allow the individual members of the swarm to communicate and allocate tasks amongst themselves, plan their trajectories, and coordinate their flight in such a way that the overall objectives of the swarm are achieved efficiently. These algorithms, often organized in a hierarchical fashion, endow the swarm with autonomy at every level, and the role of a human operator can be reduced, in principle, to interactions at a higher level without direct intervention. This technology depends on the clever and innovative application of theoretical tools from control and estimation. This paper reviews the state of the art of these theoretical tools, specifically focusing on how they have been developed for, and applied to, aerial swarms. Aerial swarms differ from swarms of ground-based vehicles in two respects: they operate in a three-dimensional space and the dynamics of individual vehicles adds an extra layer of complexity. We review dynamic modeling and conditions for stability and controllability that are essential in order to achieve cooperative flight and distributed sensing. The main sections of this paper focus on major results covering trajectory generation, task allocation, adversarial control, distributed sensing, monitoring, and mapping. Wherever possible, we indicate how the physics and subsystem technologies of aerial robots are brought to bear on these individual areas.

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A Survey on Aerial Swarm Robotics

We describe a method for multirobot trajectory planning in known, obstacle-rich environments. We demonstrate our approach on a quadrotor swarm navigating in a warehouse setting. Our method consists of following three stages: 1) roadmap generation that generates sparse roadmaps annotated with possible interrobot collisions; 2) discrete planning that finds valid execution schedules in discrete time and space; 3) continuous refinement that creates smooth trajectories. We account for the downwash effect of quadrotors, allowing safe flight in dense formations. We demonstrate computational efficiency in simulation with up to 200 robots and physical plausibility with an experiment on 32 nano-quadrotors. Our approach can compute safe and smooth trajectories for hundreds of quadrotors in dense environments with obstacles in a few minutes.

Trajectory Planning for Quadrotor Swarms

Enclosing a target by nonholonomic mobile robots with bearing-only measurements

Robotic technologies, whether they are remotely operated vehicles, autonomous agents, assistive devices, or novel control interfaces, offer many promising capabilities for deployment in real world environments. Post-disaster scenarios are a particularly relevant target for applying such technologies, due to the challenging conditions faced by rescue workers and the possibility to increase their efficacy while decreasing the risks they face. However, fielddeployable technologies for rescue work have requirements for robustness, speed, versatility, and ease of use that may not be matched by the state of the art in robotics research. This paper aims to survey the current state of the art in ground and aerial robots, marine and amphibious systems, and human-robot control interfaces and assess the readiness of these technologies with respect to the needs of first responders and disaster recovery efforts. We have gathered expert opinions from emergency response stakeholders and researchers who conduct field deployments with them in order to understand these needs, and we present this assessment as a way to guide future research toward technologies that will make an impact in real world disaster response and recovery.

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The current state and future outlook of rescue robotics

In this paper, we present a trajectory planning method to navigate a quadrotor with a cable-suspended payload through known obstacle-filled environments. We model the system as a hybrid dynamical system and formulate the trajectory generation problem as a Mixed Integer Quadratic Program (MIQP). Specifically, we address two novel challenges. First, we plan for a multi-body system, and obstacle avoidance must be guaranteed for the quadrotor, load, and the cable. Second, our method accommodates transitions between subsystems of the hybrid dynamical system, allowing for maneuvers that would otherwise be infeasible if the cable were constrained to remain taut. Numerical and experimental results validate the proposed approach for the full hybrid system.

Mixed Integer Quadratic Program trajectory generation for a quadrotor with a cable-suspended payload

We address the problem of high speed autonomous navigation of quadrotor micro aerial vehicles with limited onboard sensing and computation. In particular, we propose a dual range planning horizon method to safely and quickly navigate quadrotors to specified goal locations in previously unknown and unstructured environments. In each planning epoch, a short-range planner uses a local map to generate a new trajectory. At the same time, a safe stopping policy is found. This allows the robot to come to an emergency halt when necessary. Our algorithm guarantees collision avoidance and demonstrates important advances in real-time planning. First, our novel short range planning method allows us to generate and re-plan trajectories that are dynamically feasible, comply with state and input constraints, and avoid obstacles in real-time. Further, previous planning algorithms abstract away the obstacle detection problem by assuming the instantaneous availability of geometric information about the environment. In contrast, our method addresses the challenge of using the raw sensor data to form a map and navigate in real-time. Finally, in addition to simulation examples, we provide physical experiments that demonstrate the entire algorithmic pipeline from obstacle detection to trajectory execution.

High speed navigation for quadrotors with limited onboard sensing

Payload manipulation with aerial robots has been an active research area for many years. Recent approaches have sought to plan, control, and execute maneuvers with large, yet deliberate, load swings for more agile, energy-optimal maneuvering. Unfortunately, the system's nonlinear dynamics make executing such trajectories a significant challenge and experimental demonstrations thus far have relied completely on a motion capture system and non-negligible simplifications like restriction of the system to a two-dimensional workspace or closing of the control loop on the quadrotor, instead of the payload. In this work, we observe the payload using a downward-facing camera and estimate its state relative to the quadrotor using an extended Kalman filter. We demonstrate closed-loop payload control in the full three-dimensional workspace, with the planning, estimation, and control pipeline implemented on an onboard processor. We show control of load swings up to 53o from the vertical axis. To the best of our knowledge, this represents the first realization of closed-loop control of agile slung-load maneuvers and the largest achieved payload angle.

Aggressive Flight With Suspended Payloads Using Vision-Based Control

In this work, we present Hold Or take Optimal Plan (HOOP), a centralized trajectory generation algorithm for labeled multi-robot systems operating in obstacle-free, two-dimensional, continuous work...

Hold Or take Optimal Plan (HOOP): A quadratic programming approach to multi-robot trajectory generation:

In this paper, we consider the problem of planning collision-free trajectories to navigate a team of labeled robots from a set of start locations to a set of goal locations, where robots have pre-assigned and non-interchangeable goals. We present a solution to this problem for a centralized team operating in an obstacle-free, two-dimensional workspace. Our algorithm allows robots to follow Optimal Motion Plans (OMPs) to their goals when possible and has them enter Circular HOlding Patterns (CHOPs) to safely navigate congested areas. This OMP\(+\)CHOP algorithm is shown to be safe and complete, and simulation results show scalability to hundreds of robots.

Sarah Y. Tang

Papers

Mixed Integer Quadratic Program trajectory generation for a quadrotor with a cable-suspended payload

High speed navigation for quadrotors with limited onboard sensing

Aggressive Flight With Suspended Payloads Using Vision-Based Control

Hold Or take Optimal Plan (HOOP): A quadratic programming approach to multi-robot trajectory generation:

A Complete Algorithm for Generating Safe Trajectories for Multi-robot Teams