The mechanical simplicity, hover capabilities, and high agility of quadrotors lead to a fast adaption in the industry for inspection, exploration, and urban aerial mobility. On the other hand, the unstable and underactuated dynamics of quadrotors render them highly susceptible to system faults, especially rotor failures. In this work, we propose a fault-tolerant controller using nonlinear model predictive control (NMPC) to stabilize and control a quadrotor subjected to the complete failure of a single rotor. Differently from existing works, which either rely on linear assumptions or resort to cascaded structures neglecting input constraints in the outer-loop, our method leverages full nonlinear dynamics of the damaged quadrotor and considers the thrust constraint of each rotor. Hence, this method could effectively perform upset recovery from extreme initial conditions. Extensive simulations and real-world experiments are conducted for validation, which demonstrates that the proposed NMPC method can effectively recover the damaged quadrotor even if the failure occurs during aggressive maneuvers, such as flipping and tracking agile trajectories.
We present the design of a robotic leg that can seamlessly switch between a spring-suspended-, and unsuspended configuration. Switching is realized by a mechanism that exploits the alternative configuration of the two-link leg. The mechanism is lightweight, does not require additional actuation, and only relies on the leg movement for engagement. We validated the performance of the prototype leg on a single-leg testbed and investigated the power consumption during standing, crouching, and hopping in both configurations. The experiments showed that the efficiency of hopping and cyclic base height control is better with the spring-suspended configuration. However, it can undermine the leg's performance in position control and requires higher torque to maintain low base height, where the unsuspended configuration has advantages. Overall, the switching ability allows for seamlessly selecting the optimal mode for a specific locomotion task.
The reliable and efficient self-adaptive analysis is a modern goal of various numerical computations. Most adaptivity methods, however, adopt energy norm to measure errors, which may not be the most natural and convenient means, e.g., for problems with locally singular gradient of displacement. Based on the Element Energy Projection (EEP) super-convergent technique in the Finite Element Method of Lines (FEMOL) which is a general and powerful semi-discrete method, reliable error estimates of displacements in maximum norm can be obtained anywhere on the FEMOL mesh and hence adaptive FEMOL by maximum norm becomes feasible. However, to tackle singularity problems effectively and efficiently, an automatic and flexible local mesh refinement strategy is required to generate meshes of high quality for more efficient adaptive FEMOL analysis. Taking the two-dimensional Poisson equation as the model problem, the paper firstly introduces the FEMOL and EEP methods with interface sides resulting from local mesh refinement. Then a local mesh refinement strategy and corresponding adaptive algorithm are presented. The numerical results given show that the proposed adaptive FEMOL with local mesh refinement can produce displacement solutions satisfying the specified tolerances in maximum norm and the adaptively-generated meshes reasonably reflect the local difficulties inherent in the physical problems without much redundant accuracy.
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