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Collision avoidance is a key technology enabling applications such as autonomous vehicles and robots. Various reinforcement learning techniques such as the popular Q-learning algorithms have emerged as a promising solution for collision avoidance in robotics. While spiking neural networks (SNNs), the third generation model of neural networks, have gained increased interest due to their closer resemblance to biological neural circuits in the brain, the application of SNNs to mobile robot navigation has not been well studied. Under the context of reinforcement learning, this paper aims to investigate the potential of biologically-motivated spiking neural networks for goal-directed collision avoidance in reasonably complex environments. Unlike the existing additive reward-modulated spike timing dependent plasticity learning rule (A-RM-STDP), for the first time, we explore a new multiplicative RM-STDP scheme (M-RM-STDP) for the targeted application. Furthermore, we propose a more biologically plausible feed-forward spiking neural network architecture with fine-grained global rewards. Finally, by combining the above two techniques we demonstrate a further improved solution to collision avoidance. Our proposed approaches not only completely outperform Q-learning for cases where Q-learning can hardly reach the target without collision, but also significantly outperform a baseline SNN with A-RMSTDP in terms of both success rate and the quality of navigation trajectories.