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The role of a motion planner is pivotal in quadrotor applications, yet existing methods often struggle to adapt to complex environments, limiting their ability to achieve fast, safe, and robust flight. In this letter, we introduce a performance-enhanced quadrotor motion planner designed for autonomous flight in complex environments including dense obstacles, dynamic obstacles, and unknown disturbances. The global planner generates an initial trajectory through kinodynamic path searching and refines it using B-spline trajectory optimization. Subsequently, the local planner takes into account the quadrotor dynamics, estimated disturbance, global reference trajectory, control cost, time cost, and safety constraints to generate real-time control inputs, utilizing the framework of model predictive contouring control. Both simulations and real-world experiments corroborate the heightened robustness, safety, and speed of the proposed motion planner. Additionally, our motion planner achieves flights at more than 6.8 m/s in a challenging and complex racing scenario.

For real-world navigation, it is important to endow robots with the capabilities to navigate safely and efficiently in a complex environment with both dynamic and non-convex static obstacles. However, achieving path-finding in non-convex complex environments without maps as well as enabling multiple robots to follow social rules for obstacle avoidance remains challenging problems. In this letter, we propose a socially aware robot mapless navigation algorithm, namely Safe Reinforcement Learning-Optimal Reciprocal Collision Avoidance (SRL-ORCA). This is a multi-agent safe reinforcement learning algorithm by using ORCA as an external knowledge to provide a safety guarantee. This algorithm further introduces traffic norms of human society to improve social comfort and achieve cooperative avoidance by following human social customs. The result of experiments shows that SRL-ORCA learns strategies to obey specific traffic rules. Compared to DRL, SRL-ORCA shows a significant improvement in navigation success rate in different complex scenarios mixed with the application of the same training network. SRL-ORCA is able to cope with non-convex obstacle environments without falling into local minimal regions and has a 14.1\% improvement in path quality (i.e., the average time to target) compared to ORCA. Videos are available at https://youtu.be/huhXfCDkGws.

This paper investigates the problem of securing exponentially fast consensus (exponential consensus for short) for identical agents with finite-dimensional linear system dynamics over dynamic network topology. Our aim is to find the weakest possible conditions that guarantee exponentially fast consensus using a Lyapunov function consisting of a sum of terms of the same functional form. We first investigate necessary conditions, starting by examining the system (both agent and network) parameters. It is found that controllability of the linear agents is necessary for reaching consensus. Then, to work out necessary conditions incorporating the network topology, we construct a set of Laplacian matrix-valued functions. The precompactness of this set of functions is shown to be a significant generalization of existing assumptions on network topology, including the common assumption that the edge weights are bounded piecewise constant functions or continuous functions. With the aid of such a precompactness assumption and restricting the Lyapunov function to one consisting of a sum of terms of the same functional form, we prove that a joint $(\delta, T)$-connectivity condition on the network topology is necessary for exponential consensus. Finally, we investigate how the above two ``necessities'' work together to guarantee exponential consensus. To partially address this problem, we define a synchronization index to characterize the interplay between agent parameters and network topology. Based on this notion, it is shown that by designing a proper feedback matrix and under the precompactness assumption, exponential consensus can be reached globally and uniformly if the joint $(\delta,T)$-connectivity and controllability conditions are satisfied, and the synchronization index is not less than one.

In this paper, we aim to investigate the synchronization problem of dynamical systems, which can be of generic linear or Lipschitz nonlinear type, communicating over directed switching network topologies. A mild connectivity assumption on the switching topologies is imposed, which allows them to be directed and jointly connected. We propose a novel analysis framework from both algebraic and geometric perspectives to justify the attractiveness of the synchronization manifold. Specifically, it is proven that the complementary space of the synchronization manifold can be spanned by certain subspaces. These subspaces can be the eigenspaces of the nonzero eigenvalues of Laplacian matrices in linear case. They can also be subspaces in which the projection of the nonlinear self-dynamics still retains the Lipschitz property. This allows to project the states of the dynamical systems into these subspaces and transform the synchronization problem under consideration equivalently into a convergence one of the projected states in each subspace. Then, assuming the joint connectivity condition on the communication topologies, we are able to work out a simple yet effective and unified convergence analysis for both types of dynamical systems. More specifically, for partial-state coupled generic linear systems, it is proven that synchronization can be reached if an extra condition, which is easy to verify in several cases, on the system dynamics is satisfied. For Lipschitz-type nonlinear systems with positive-definite inner coupling matrix, synchronization is realized if the coupling strength is strong enough to stabilize the evolution of the projected states in each subspace under certain conditions., Comment: 17 pages, 11 figures