  In this paper, we investigate the fixed-time behavioral control problem for a
team of second-order nonlinear agents, aiming to achieve a desired formation
with collision/obstacle~avoidance. In the proposed approach, the two
behaviors(tasks) for each agent are prioritized and integrated via the
framework of the null-space-based behavioral projection, leading to a desired
merged velocity that guarantees the fixed-time convergence of task errors. To
track this desired velocity, we design a fixed-time sliding mode controller for
each agent with state-independent adaptive gains, which provides a fixed-time
convergence of the tracking error. The control scheme is implemented in a
distributed manner, where each agent only acquires information from its
neighbors in the network. Moreover, we adopt an online learning algorithm to
improve the robustness of the closed system with respect to
uncertainties/disturbances. Finally, simulation results are provided to show
the effectiveness of the proposed approach.
