Safety guarantee prior to the deployment of robots can be difficult due to unexpected disturbances in runtime. This article presents a real-time receding-horizon robust trajectory planning algorithm for nonlinear closed-loop systems, which guarantees the safety of the system under unknown but bounded disturbances. We characterize the forward reachable sets (FRSs) of the system based on the Hamilton–Jacobi reachability analysis as a means for safety verification. For the online computation of the FRSs, we approximate nonlinear systems as LTV systems with linearization errors and compute ellipsoids that encompass the FRSs in continuous time. Using the proposed ellipsoidal approximation of the FRSs, we formulate a computationally tractable robust planning problem that can be solved online. Consequently, the proposed method enables real-time replanning of a reference trajectory with safety guarantees even when the system encounters unexpected disturbances in runtime. The flight experiment of obstacle avoidance in a windy environment validates the proposed robust planning algorithm.

Planning a trajectory with guaranteed safety is a core part for a risk-free flight of a multirotor. If a trajectory planner only aims to ensure safety, it may generate trajectories which overly bypass risky regions and prevent the system from achieving specific missions. This work presents a robust trajectory planning algorithm which simultaneously guarantees the safety and reachability to the target state in the presence of unknown disturbances. We first characterize how the forward and backward reachable sets (FRSs and BRSs) are constructed by using Hamilton-Jacobi reachability analysis. Based on the analysis, we present analytic expressions for the reachable sets and then propose minimal ellipsoids which closely approximate the reachable sets. In the planning process, we optimize the reference trajectory to connect the FRSs and BRSs, while avoiding obstacles. By combining the FRSs and BRSs, we can guarantee that any state inside of the initial set reaches the target set. We validate the proposed algorithm through a simulation of traversing a narrow gap.

This study addresses an operation of unmanned aerial vehicles (UAVs) in a network environment where there is time-varying network delay. The network delay entails undesirable effects on the stability of the UAV control system due to delayed state feedback and outdated control input. Although several networked control algorithms have been proposed to deal with the network delay, most existing studies have assumed that the plant dynamics is known and simple, or the network delay is constant. These assumptions are improper to multirotor-type UAVs because of their nonlinearity and time-sensitive characteristics. To deal with these problems, we propose a networked control system using model predictive control (MPC) designed under the consideration of multirotor characteristics. We also apply a Gaussian process (GP) to learn an unknown nonlinear model, which increases the accuracy of path planning and state estimation. Flight experiments show that the proposed algorithm successfully compensates the network delay and Gaussian process learning improves the UAV's path tracking performance.

This paper presents planning and control algorithms for a multi-rotor with a suspended load. The suspended load cannot be controlled easily by the multi-rotor due to severe dynamic coupling between them. Difficulties are exacerbated by under-actuated, highly nonlinear nature of multi-rotor dynamics. Although many studies have been proposed to plan trajectories and control this system, there exist only a few reports on real-time trajectory generation. With this in mind, we propose a planning method which is capable of generating collision-free trajectories real-time and applicable to a high-dimensional nonlinear system. Using a differential flatness property, the system can be linearized entirely with elaborately chosen flat outputs. Convexification of non-convex constraints is carried out, and concave obstacle-avoidance constraints are converted to convex ones. After that, a convex optimization problem is solved to generate an optimal trajectory, but semi-feasible trajectory which considers only some parts of the initial state. We apply model predictive control with a sequential linear quadratic solver to compute a feasible collision-free trajectory and to control the system. Performance of the algorithm is validated by flight experiment.

In the paper, we propose a robust real-time visual odometry in dynamic environments via rigid-motion model updated by scene flow. The proposed algorithm consists of spatial motion segmentation and temporal motion tracking. The spatial segmentation first generates several motion hypotheses by using a grid-based scene flow and clusters the extracted motion hypotheses, separating objects that move independently of one another. Further, we use a dual-mode motion model to consistently distinguish between the static and dynamic parts in the temporal motion tracking stage. Finally, the proposed algorithm estimates the pose of a camera by taking advantage of the region classified as static parts. In order to evaluate the performance of visual odometry under the existence of dynamic rigid objects, we use self-collected dataset containing RGB-D images and motion capture data for ground-truth. We compare our algorithm with state-of-the-art visual odometry algorithms. The validation results suggest that the proposed algorithm can estimate the pose of a camera robustly and accurately in dynamic environments.

Ensuring safety in trajectory planning of multirotor systems is an essential element for risk-free operation. Even if the generated trajectory is known to be safe in the planning phase, unknown disturbance during an actual operation can lead to a dangerous situation. This paper proposes safety-guaranteed receding horizon planning against unknown, but bounded, disturbances. We first characterize forward reachable set (FRS) of the system, the set of states after a certain duration considering all possible disturbances, using Hamilton-Jacobi (HJ) reachability analysis. To compute the FRSs in real-time, we conservatively approximate the true FRS and perform ellipsoidal parameterization on the FRSs. Using the FRSs, we can plan a robust trajectory that avoids risky regions and rapidly re-plan the trajectory when the system encounters sudden disturbance. The proposed method is validated through an experiment of avoiding obstacles in a wind.

This paper investigates a multi-rotor with a suspended load in perspectives of 1) real-time path planning, 2) obstacle avoidance, and 3) transportation of a suspended object. A suspended load cannot be controlled with conventional controllers designed for nominal multi-rotors due to the dynamic coupling between the multi-rotor and load. Although several control and planning algorithms have been proposed based on elaborately derived dynamic equations, most existing studies separate control and path planning problems by following predefined trajectories after trajectory generation. Moreover, many state-of-the-art trajectory generation algorithms cannot work real-time for a system with high degrees of freedom, which makes it not suitable to operate the system in dynamic environments where obstacles appear abruptly or move unexpectedly. With this in mind, we apply Model Predictive Control (MPC) with Sequential Linear Quadratic (SLQ) solver to compute feasible and optimal trajectory real-time and to operate a multi-rotor with a suspended load in dynamic environments. We design an obstacle-avoidance algorithm suitable for the current platform flying in cluttered environments. Flight experiments shows that the proposed algorithm successfully controls the multi-rotor and allows to avoid obstacles simultaneously.