YAT Anshin! Uchuu Ryoukou [TV]

From the Wikipedia Article:

The human civilization has taken gigantic steps in the conquest of the space. For 15 years, with the creation of the three-dimensional Tunnel, they can travel to any Galaxy in the universe.“The Gentleman of the Cosmos” is the company that manages the three-dimensional tunnel and dominates organizes the trips. Many companies follow ahead. One of those small companies is YAT (“Yamamoto Anshin Travel”), commanded by Yamamoto, and his beautiful daughter Katsura, her foreign pet lizard Bucky who is the mascot of the company, the robot, Kanabe who navigates and Utchi, the extraterrestrial pilot, and Goro Hoshiwatari, an adolescent who has left his home to travel by the space and to find the whereabouts of his father, who disappeared fifteen years ago during the explosion of the main transporting center of the three-dimensional Tunnel that he created. Goro falls in love with Katsura, and becomes the YAT mechanic/janitor after an accident that he was responsible for, so he tags along to pay for the damage, as well to find his father. But to find his father will not be his only problem, since Kanea, a young lady whose mother is the owner of “the Gentleman of the Cosmos”, is in love with him. In addition, Kanea’s mother had a mysterious and conflicting past with Yamamoto.