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People tracking and following has become an increasingly popular research topic in recent years. In this paper, two target following methods are proposed and compared. The first is an intuitive method, it sets a pseudo goal further away than the actual target location and use obstacle avoidance algorithm to reach the pseudo goal. The second method uses heuristic search to find a trajectory which can maximize target visibility and minimize the distance between robot and target at the same time. Experimental results show that the proposed trajectory optimization method greatly outperforms the intuitive approach.