Many autonomous tasks can be considered as having to satisfy multiple goals simultaneously. In particular, Autonomous Vehicle (AV) navigation can be considered as a task having to satisfy at least two goals in an environment. The first goal is to plan a path for an agent to move from an origin to a destination that takes the shortest number of navigation steps. If the environment is static and the destination is stationary, then this shortest path is constant and can be planned in advance if the environment is known a priori, or estimated as the agent explores the environment if it is initially unknown. If the environment or the destination is dynamically changing, then the shortest path is no longer constant. This problem may still be considered as a path planning issue if the environment at each sampled time is known. However, the problem is more appropriately dealt with by incorporating a second goal that aims to avoid collisions between the agent and its neighboring obstacles while executing an overall shortest path strategy towards the destination. The collision avoidance (CA) problem has been well studied in the context of static known or unknown environments (Latombe, 1991; Ge & Cui, 2000; Oriolo et al., 1998; Ye et al., 2003). In the case of dynamic environments (DE) (Stentz, 1994; Stentz, 1995; Yang & Meng, 2003; Minguez & Minguez, 2004; Minguez, 2005), the focus at present is on dynamic environment (DE) that is slowly changing with fairly low obstacle density. In theory, if the agent samples the environment fast enough, any environment would appear as a static environment and the navigation problem can be solved using existing solutions for static environments. In practice, this condition is difficult to achieve particularly when obstacles are moving at speeds higher than the agent or sampling rate is low. To deal with this situation, an obvious approach is to explicitly consider obstacle motions. Fiorini & Shiller (Fiorini & Shiller, 1998) proposed the concept of Velocity Obstacles that enables obstacle motions between two time steps to be considered in their formulation. Like other similar algorithms (Mucientes e al., 2001; Yamamoto et al., 2001; Feng et al., 2004; Qu et al., 2004), they assumed that objects move in a constant velocity. Shiller et al. (Shiller et al., 2001; Large et al., 2002) further proposed the non-linear velocity obstacle concept which assumes that obstacles can have variable speed. Moreover, they described the obstacles’ trajectories using circular approximation. Although it may not always capture the correct movement of obstacles, it is an attempt to predict obstacle motions between two time steps. Similarly, Zhu’s hidden Markov model (Zhu, 1991) and Miura’s probabilistic model (Miura et al., 1999) also attempted the same. The idea of considering obstacles motion within two time steps explicitly proves to be vital in enhancing the agent’s CA ability in reality. Motivated by
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