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In this article, we present an optimization-based framework for multicopter trajectory planning subject to geometrical configuration constraints and user-defined dynamic constraints. The basis of the framework is a novel trajectory representation built upon our novel optimality conditions for unconstrained control effort minimization. We design linear-complexity operations on this representation to conduct spatial–temporal deformation under various planning requirements. Smooth maps are utilized to exactly eliminate geometrical constraints in a lightweight fashion. A variety of state-input constraints are supported by the decoupling of dense constraint evaluation from sparse parameterization and the backward differentiation of flatness map. As a result, this framework transforms a generally constrained multicopter planning problem into an unconstrained optimization that can be solved reliably and efficiently. Our framework bridges the gaps among solution quality, planning efficiency, and constraint fidelity for a multicopter with limited resources and maneuvering capability. Its generality and robustness are both demonstrated by applications to different flight tasks. Extensive simulations and benchmarks are also conducted to show its capability of generating high-quality solutions while retaining the computation speed against other specialized methods by orders of magnitude. [ABSTRACT FROM AUTHOR]

Planning high-speed trajectories for UAVs in unknown environments requires algorithmic techniques that enable fast reaction times to guarantee safety as more information about the environment becomes available. The standard approaches that ensure safety by enforcing a “stop” condition in the free-known space can severely limit the speed of the vehicle, especially in situations where much of the world is unknown. Moreover, the ad-hoc time and interval allocation scheme usually imposed on the trajectory also leads to conservative and slower trajectories. This work proposes FASTER (Fast and Safe Trajectory Planner) to ensure safety without sacrificing speed. FASTER obtains high-speed trajectories by enabling the local planner to optimize in both the free-known and unknown spaces. Safety is ensured by always having a safe back-up trajectory in the free-known space. The MIQP formulation proposed also allows the solver to choose the trajectory interval allocation. FASTER is tested extensively in simulation and in real hardware, showing flights in unknown cluttered environments with velocities up to 7.8 m/s, and experiments at the maximum speed of a skid-steer ground robot (2 m/s). [ABSTRACT FROM AUTHOR]

This article presents MADER, a 3-D decentralized and asynchronous trajectory planner for UAVs that generates collision-free trajectories in environments with static obstacles, dynamic obstacles, and other planning agents. Real-time collision avoidance with other dynamic obstacles or agents is done by performing outer polyhedral representations of every interval of the trajectories and then including the plane that separates each pair of polyhedra as a decision variable in the optimization problem. MADER uses our recently developed MINVO basis to obtain outer polyhedral representations with volumes 2.36 and 254.9 times, respectively, smaller than the Bernstein or B-Spline bases used extensively in the planning literature. Our decentralized and asynchronous algorithm guarantees safety with respect to other agents by including their committed trajectories as constraints in the optimization and then executing a collision check-recheck scheme. Finally, extensive simulations in challenging cluttered environments show up to a 33.9% reduction in the flight time, and a 88.8% reduction in the number of stops compared to the Bernstein and B-Spline bases, shorter flight distances than centralized approaches, and shorter total times on average than synchronous decentralized approaches. [ABSTRACT FROM AUTHOR]

This article presents a distributed, efficient, scalable, and real-time motion planning algorithm for a large group of agents moving in 2-D or 3-D spaces. This algorithm enables autonomous agents to generate individual trajectories independently with only the relative position information of neighboring agents. Each agent applies a force-based control that contains two main terms: 1) collision avoidance and 2) navigational feedback. The first term keeps two agents separate with a certain distance, while the second term attracts each agent toward its goal location. Compared with existing collision-avoidance algorithms, the proposed force-based motion planning (FMP) algorithm can find collision-free motions with lower transition time, free from velocity state information of neighboring agents. It leads to less computational overhead. The performance of proposed FMP is examined over several dense and complex 2-D and 3-D benchmark simulation scenarios, with results outperforming existing methods. [ABSTRACT FROM AUTHOR]

Recent advances in trajectory replanning have enabled quadrotor to navigate autonomously in unknown environments. However, high-speed navigation still remains a significant challenge. Given very limited time, existing methods have no strong guarantee on the feasibility or quality of the solutions. Moreover, most methods do not consider environment perception, which is the key bottleneck to fast flight. In this article, we present RAPTOR, a robust and perception-aware replanning framework to support fast and safe flight, which addresses these issues systematically. A path-guided optimization approach that incorporates multiple topological paths is devised, to ensure finding feasible and high-quality trajectories in very limited time. We also introduce two perception-aware planning approaches to actively observe and avoid unknown obstacles. A risk-aware trajectory refinement ensures that unknown obstacles which may endanger the quadrotor can be observed earlier and avoid in time. The motion of yaw angle is planned to actively explore the surrounding space that is relevant for safe navigation. The proposed methods are tested extensively through benchmark comparisons and challenging indoor and outdoor aggressive flights. We release our implementation as an open-source package1 for the community. [ABSTRACT FROM AUTHOR]

In this article, we propose a nonlinear receding horizon game-theoretic planner for autonomous cars in competitive scenarios with other cars. The online planner is specifically formulated for a multiple-car autonomous racing game, in which each car tries to advance along a given track as far as possible with respect to the other cars. The algorithm extends previous work on game-theoretic planning for single-integrator agents to be suitable for autonomous cars in the following ways: 1) by representing the trajectory as a piecewise polynomial; 2) incorporating bicycle kinematics into the trajectory; and 3) enforcing constraints on path curvature and acceleration. The game-theoretic planner iteratively plans a trajectory for the ego vehicle and then the other vehicles in sequence until convergence. Crucially, the trajectory optimization includes a sensitivity term that allows the ego vehicle to reason about how much the other vehicles will yield to the ego vehicle to avoid collisions. The resulting trajectories for the ego vehicle exhibit rich game strategies such as blocking, faking, and opportunistic overtaking. The game-theoretic planner is shown to significantly outperform a baseline planner using model-predictive control, which does not take interaction into account. The performance is validated in high-fidelity numerical simulations with three cars, in experiments with two small-scale autonomous cars, and in experiments with a full-scale autonomous car racing against a simulated vehicle (video is available at https://youtube.com/playlist?list=PLmIcLEh8KMje4rYBqRANDuKvqFvj7LCRp). [ABSTRACT FROM AUTHOR]

This article proposes a computational trajectory optimization framework for solving the problem of multiobjective automatic parking motion planning. Constrained automatic parking maneuver problem is usually difficult to solve because of some practical limitations and requirements. This problem becomes more challenging when multiple objectives are required to be optimized simultaneously. The designed approach employs a swarm intelligent algorithm to produce the tradeoff front along the objective space. In order to enhance the local search ability of the algorithm, a gradient operation is utilized to update the solution. In addition, since the evolutionary process tends to be sensitive with respect to the flight control parameters, a novel adaptive parameter controller is designed and incorporated in the algorithm framework such that the proposed method can dynamically balance the exploitation and exploration. The performance of using the designed multiobjective strategy is validated and analyzed by performing a number of simulation and experimental studies. The results indicate that the present approach can provide reliable solutions and it can outperform other existing approaches investigated in this article. [ABSTRACT FROM AUTHOR]

The wheeled inverted pendulum (WIP) is an underactuated, nonholonomic mechatronic system, and has been popularized commercially as the Segway. Designing a control law for motion planning, that incorporates the state and control constraints, while respecting the configuration manifold, is a challenging problem. In this article, we derive a discrete-time model of the WIP system using discrete mechanics and generate optimal trajectories for the WIP system by solving a discrete-time constrained optimal control problem. Furthermore, we describe a nonlinear continuous-time model with parameters for designing a closed-loop linear–quadratic regulator (LQR). A dual control architecture is implemented in which the designed optimal trajectory is, then, provided as a reference to the robot with the optimal control trajectory as a feedforward control action, and an LQR in the feedback mode is employed to mitigate noise and disturbances for ensuing stable motion of the WIP system. While performing experiments on the WIP system involving aggressive maneuvers with fairly sharp turns, we found a high degree of congruence in the designed optimal trajectories and the path traced by the robot while tracking these trajectories. This corroborates the validity of the nonlinear model and the control scheme. Finally, these experiments demonstrate the highly nonlinear nature of the WIP system and robustness of the control scheme. [ABSTRACT FROM AUTHOR]

Trajectory replanning for quadrotors is essential to enable fully autonomous flight in unknown environments. Hierarchical motion planning frameworks, which combine path planning with path parameterization, are popular due to their time efficiency. However, the path planning cannot properly deal with nonstatic initial states of the quadrotor, which may result in nonsmooth or even dynamically infeasible trajectories. In this article, we present an efficient kinodynamic replanning framework by exploiting the advantageous properties of the B-spline, which facilitates dealing with the nonstatic state and guarantees safety and dynamical feasibility. Our framework starts with an efficient B-spline-based kinodynamic (EBK) search algorithm, which finds a feasible trajectory with minimum control effort and time. To compensate for the discretization induced by the EBK search, an elastic optimization approach is proposed to refine the control point placement to the optimal location. Systematic comparisons against the state-of-the-art are conducted to validate the performance. Comprehensive onboard experiments using two different vision-based quadrotors are carried out showing the general applicability of the framework. [ABSTRACT FROM AUTHOR]

Motion planning is one of the most critical problems in multirobot systems. The basic target is to generate a collision-free trajectory for each robot from its initial position to the target position. In this paper, we study the trajectory planning for the multirobot systems operating in unstructured and changing environments. Each robot is equipped with some sensors of limited sensing ranges. We propose a fully distributed approach to planning trajectories for such systems. It combines the model predictive control (MPC) strategy and the incremental sequential convex programming (iSCP) method. The MPC framework is applied to detect the local running environment real-timely with the concept of receding horizon. For each robot, a nonlinear programming is built in its current prediction horizon. To construct its own optimization problem, a robot first needs to communicate with its neighbors to retrieve their current states. Then, the robot predicts the neighbors’ future positions in the current horizon and constructs the problem without waiting for the prediction information from its neighbors. At last, each robot solves its problem independently via the iSCP method such that the robot can move autonomously. The proposed method is polynomial in its computational complexity. [ABSTRACT FROM AUTHOR]

Avionics and air traffic management (ATM) systems are evolving with the introduction of progressively higher levels of automation, toward attaining the ambitious operational, technical, and safety enhancements required to sustain the present growth of global air traffic. This paper presents novel 4-Dimensional Trajectory (4DT) functionalities that are being developed for integration in ATM and avionics systems to support trajectory based operations (TBO). The 4DT planning process, which is the main focus of the paper, is supported by a custom multiobjective variant of state-of-the-art optimal control algorithms, incorporating various operational, economic, and environmental factors. Capitalizing on the higher theoretical accuracy offered by optimal control algorithms compared to other methods, a key feature of the proposed approach is the introduction of a postprocessing stage to ensure that the mathematically optimal trajectories are translated into a set of standardized 4DT descriptors, which can be flown by state-of-the-art automatic flight control systems. Additionally, to support air-ground 4DT intent negotiation and validation in the TBO context, the 4DT postprocessing ensures that optimal trajectories are synthetically described by a limited number of parameters, minimizing the bandwidth requirements imposed on airborne data links. Simulation-based verification activities addressing operational efficiency improvements and computational performance in the terminal area ATM context support the viability of the proposed 4DT planning functionality for online tactical TBO. [ABSTRACT FROM AUTHOR]

We propose an efficient time-optimal trajectory planning algorithm for an environment with multiple static circular obstacles, which is based on dynamics for differential-wheeled mobile robots (DWMRs) including actuators. This problem is known to be complex particularly if obstacles are present and if full dynamics including actuators is considered. Given a geometric corridor, the proposed technique defines a portion of trajectory between obstacles as a section which is constituted of an arc, out-curve, and in-curve, each with constant control input satisfying bang–bang principle for time-optimization. Then, it designs time-optimal trajectory composed of multiple sections using common tangent between two tangent circles, in which it handles multiple consecutive obstacles without arcs. This method helps to treat complex environment considering dynamics with DWMR's actuators. Simulation results are shown to validate the efficiency of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a novel offline minimum-time trajectory planning (MTTP) approach for underactuated overhead cranes. To the best of our knowledge, it is the first optimal solution to the MTTP problem for overhead crane systems, which simultaneously takes into account various constraints, including the bounded swing angle for the payload, bounded velocity, acceleration, and even jerk for the trolley. Different from existing approaches, by means of system discretization and augmentation, the quasi-convex optimization technique is successfully adopted to find the minimum-time solution while satisfying all the aforementioned constraints. Extensive simulation and experiments with comparisons to previously published methods are conducted to show the superior performance of the proposed method. Note that the results derived in this paper also serve as promising guidance in engineering applications, since it provides a performance limit, namely, the possible highest efficiency for automatic or manual operation of overhead cranes. [ABSTRACT FROM PUBLISHER]