Big Brother Instinct: All of the mechs feel this towards Yuuta and would do everything to protect him.
Chest Blaster: (Super) Build Tiger has such a weapon, firing the attack through the tiger's maw.
Combining Mecha: The Build Team combines into Build Tiger, and with Drillboy added in, Super Build Tiger. Deckerd and Duke combined with their respective support vehicle become J-Decker and Duke Fire. All three of the combiners in full form are gigantic. This is driven further when J-Decker and Duke Fire combine into Fire J-Decker who dwarfs even the above mentioned Combining Mecha. The original Build Team (everybody minus Drillboy) at first was unable to combine thanks to the situation — they felt pressured and nervous.
Fire-Forged Friends: From Shadowmaru's appearance on, each new member had to face their own problems integrating into the team, but their bonds have all but become stronger because of this.
Humongous Mecha: Of the sentient, non-piloted variety. The robots go a bit higher than 5 meters in their normal bodies. They have also toy bodies, however, to which their minds can be transferred when their original bodies need extensive repairs.
Ridiculously Human Robots: Every robot with the Super A.I. derived from Deckerd's mind gains human-like sentience. The designers of the Brave Police didn't intend sentient robots, and didn't even think it was possible they could gain sentience. This makes Deckerd one of the few examples who is this trope by accident regarding the "Ridiculously Human Personality" part of the equation.
Justified on two levels. 1) The Project "Brave Police" was supposed to introduce advanced robots working with human police officers and interacting with the normal populace. It makes sense to design them humanoid to enhance general acceptance. 2) Deckerd's original A.I. enabled him to understand human speech, interact on a basic level with people and work in crime investigations. Adding his humanoid body and human face and the interactions with Yuuta, it's clear why his emotions are human or very human-like at the least.
McCrane, Powerjoe and Dumpson named themselves. Their choice is justified because all three transform into construction vehicles.
Likewise, the names of the four main protagonists are taken from movie characters and stars: Deckard from Blade Runner, John MacLane from Die Hard and Bruce Lee (from a Japanese syllabic standpoint vis-a-vis Power Joe).
The Heart: Yuuta shares this role with Deckerd - they hold the team together. Despite his age, he is highly empathic and cares deeply for everyone on the team. But he also knows when it's more important to focus on their task than on their personal feelings, like the time Satan J-Decker destroyed a prison and Yuuta ordered the team to save the inmates instead of trying to follow the possessed Deckerd.
Heroic BSOD: Deckerd's refusal to regain his memories - after Yuuta hurt himself when trying to trigger them - chases the boy away, crying. He runs home, hides in his bed, and not even the news that Deckerd's mind will be re-written can snap him out of it. He pulls himself only together when the rest of the team calls for help against Victim's robot.
Kid Hero: Saejima promoted him to be the boss of the Brave Police Japan, although he is still only a child. But he is (at first) the only one able to call the unification command for the combiners and he avoids being the load by staying out of the fights. He also involves himself in investigations as much as he can.
Meaningful Name: The first kanji of Yuuta's first name is 勇, read as 'yuu'. It's the same kanji and the same reading that is used for the Brave Series 勇者シリーズ (Yuusha Series). Yuuta is literally "brave" and/or "courageous".
Tender Tears: Whenever one of his friends get hurt. He is still a child after all.
Episode 13, he neglects and verbally snaps at Deckerd, since Yuuta's archeologist parents are visiting and he'd rather focus on them. This is called out several times by pretty much everybody, and he repents fully.
Episode 28, after Deckerd decides to have his memories re-written — his claim it's Deckerd's decision what action he takes, makes his sisters and the team berate him for giving up on him.
Beware the Nice Ones: He is the most empathic, nicest person among the team, and is always professional when dealing with criminals of whatever kind. Unless people he's close to reject or ignore him big time, or loneliness is eating on him.
After Deckerd lost his memories, Yuuta is trying to jog them in the warehouse where they met each other. He slides down the vent to burst into the underground room like he used to do. But Deckerd fails to catch him, and Yuuta gets hurt at the leg yet he insists they will do it again until he remembers. At this point Deckerd snaps - screaming Enough already! as he punches a hole into the ground, then begs Yuuta in an agonized voice to stop hurting himself. The boy flees with the elevator, and he falls to his knees, asking him for forgiveness and that he doesn't want to see Yuuta suffer. After that he agrees to let Regina reprogram him.
A different version occurs in the dream episode where the Brave Police temporarily disbands. Everyone finds a new calling, except Deckerd who can't imagine a life without the Brave Police. Yuuta throws his belongings out of the Tomonaga house so Deckerd would stop clinging to his old life. Later he suffers from two illusions in the Decker Room - all of his team comrades whom invite him to a drink, and Saejima whom he bears his heart to. The last straw are two unfamiliar police mechs that mention the Brave Police disbanded save for one, stubborn robot. This causes Deckerd to run away to the warehouse where he was built, not caring that he's low on fuel and will shut-down, which will lead to his death after a short time. It is implied that not only the loss of his purpose affected him, but also the seemingly abandonment by his friends.
Hidden Depths: Deckerd handles it badly when he feels lonely. For all his competence and positive outlook, he is (at least) slightly emotional dependent on his friends and has abandoning issues. It's so bad that when he feels rejected or is separated from his friends, the worst which can happen is that he suffers a meltdown in which he becomes shockingly aggressive. One of the robot thieves in episode 13 experienced this first hand. And even in milder forms, Deckerd acts irrationally and gets easily frustrated.
Instant A.I., Just Add Water: Deckerd started as a robot with an adaptive, complex A.I. that was supposed to understand, interact and work with humans on a basic level. Yuuta treating him as a person fed his A.I. so much information to work with, it evolved over months to the point he gained intelligence, became an individual and could feel. But he could neither recognize or understand these feelings, before a final push coming from Yuuta 'wakened' his self-awareness.
Japanese Pronouns: He uses "watashi" frequently, highlighting his polite and friendly nature. Justified as he was programmed to "identify" that way — he was supposed to be a "proper policeman".
Laser-Guided Amnesia / Trauma-Induced Amnesia: Deckerd in episode 28. No wonder after the physical and emotional trauma he suffered: Being beaten near death by the two first Chieftains, then Gaizonite merged him in his injured condition with J-Decker into Satan J-Decker, then forced him into wrecking havoc and attacking his friends. Once Gaizonite fled and released his control on Deckerd, he reverted back to his injured state.
Heroic BSOD: Once Inti releases her control over McCrane and he realizes what he did, the shock makes him faint.
Hidden Depths: McCrane only uses his gun when it's necessary and is one of the most cool-headed robots on the team. However, deep down he feels vehement resentment to all criminals, whom he deems 'scum' and wishes to kill, as shown when the demon Inti possesses him. His violent outburst and intense emotions scare and disgust him, especially since he didn't think he felt such desires before.
Red Oni, Blue Oni: The blue (calm, rational) to Powerjoe's red (enthusiastic, loud). He's also the blue oni to Dumpson and Drillboy. This extends also to their actual color schemes. McCrane's primary color in robot form is a dark, rich blue; Powerjoe, Dumpson, and Drillboy sport yellow, red, and orange respectively.
Did Not Get the Girl: He has many flings in the show, but only Lua touches him so deep that he really falls in love in her. Unfortunately, she is (at least partly) only a hallucination caused by the Bubble Gum Sisters that, until the end, just he can see.
Red Oni, Blue Oni: The red oni (enthusiastic, loud) to McCrane's blue oni (calm, rational).
Robosexual: They have a mutual love for each other, they go out on dates, and she even kissed him once - although in the latter case, it's merely in Deckerd's dream in episode 40. Ayako's likely more attracted to his personality and character rather than him being a machine, however.
Highly-Visible Ninja: Shadowmaru invokes this trope only when he wants to show off. Otherwise he averts this as he operates like a real life ninja, secretly gathering intelligence and doing recon when he is sent to solo missions.
Ninja: Justified, as he actually was designed around intelligence gathering and recon. This and his aversion of Highly-Visible Ninja makes him close to a real life ninja.
Cool Bike: Gunbike. Gunmax's vehicle for patrolling, its other main purposes are either to become a jetpack armor that lets him fly or combine with him to build the Gunmax Cannon. He is so good at driving Gunbike, however, that he uses it for attacking even when it's not in a combat form.
Cool Shades: They are part of his design, but only cover his optics like any normal shades would.
Defrosting Ice King: The first to break through his shell is Yuuta in episode 20. Deckerd follows in the next episode.
Fall Guy: By manipulating video evidence, Kirisaki tried to pin the blame for crimes he committed on Gunmax just for the sake of getting Gunmax accused.
New Meat: After working closely with only one partner makes him reluctant at first to be transferred to the Brave Police. Their way of working and Yuuta's position, despite being a child, bewilder him further. Kirisaki's betrayal on top of that burnt his trust in other people, so he distances himself.
The Ace: Subverted. Regina worked to make him this, the 'perfect police man' who isn't controlled by his feelings. Duke received the best, improved traits from the other Brave Police Japan members in terms of systems, is well trained and truly competent. Most of his comrades at the Scotland Yard Brave Police adore or admire him, and he is seen as the pinnacle of current Super-A.I. development. Unlike his original team, however, the Brave Police Japan is unbiased - they instantly call him out on his arrogance the moment they meet him. The next few episodes show he isn't undefeatable either which helps him mellow out and get along with the others.
Break the Haughty: Lighter and softer version, as well as defied. Duke starts out very arrogant due to his upbringing but he realizes his flaws early on before it comes to any 'breaking', and he learns to become a better person.
Character Development: When he first joined to serve as interim leader while Deckerd was incapacitated/"dead", he was haughty, picky and generally not meshing well with the Braves. He slowly learns to get along over the next few episodes, and eventually the Japanese Brave team accepts him fully.
New Meat: The team rejects him as he's intended to replace Deckerd as the new leader. His attitude in the beginning does't help the situation either.
Theme Naming: The Knight stems from the chess theme invoked in the names of the first Scotland Yard Brave Police members that were presented to the public. The other members' names are: King, Bishop, Rook and Pawn.
Tokyo Police Department
Superintendent General Juzo Saejima (冴島・十三 Saejima Juzo)
Benevolent Boss: Crossing over with A Father to His Men. He genuinely cares about the Brave Police and their issues, defending them frequently against Azuma, stepping in for their interests and believing in them. A good example early in the show is after the original Build Team failed two times to form Build Tiger. Azuma sets the ultimatum that if this should happen a third time, Yuuta will be fired. Saejima asks the three if they think they can do it; when they say yes, he tells Azuma he will take responsibility as well should they fail, to satisfy his colleague.
Saejima also rejects the Gunpulater project once Yuuta tells him the team doesn't want the system installed into them.
Bunny-Ears Lawyer: Saejima geeks over robots, pandas and cute objects, wears a pink nightgown at home, speaks to his three robot butlers (even before meeting Deckerd), and has a vivid imagination which frequently expresses as Imagine Spots. At work, however, he's business save for some moments - that he's the Tokyo Police Department's superintendent speaks of his competence.
Cool Old Guy: He's in his forties, in top physical shape, head of the Tokyo Police Department and does his best as the Brave Police's superior to help them in any way he can and that successfully.
I Was Quite a Looker: While not that old and still attractive, Saejima was very handsome as a young man.
Mundane Made Awesome: Saejima has regular moments of this, leading to awkwardness for those present.
Real Men Wear Pink: A literal case with his pink nightgown(!) and bedcap. He has no problems wearing a pink whole-bodysuit either, or imagining himself in a school-girl uniform. In the middle of a background you would expect from a romantic shojo anime, next to Deckerd in the same uniform and a brown haired wig with a pink bow on top.
Foil: To Saejima. They respectively hold the second and highest ranking ranks of the Tokyo Police Department. Where Saejima is spirited, eccentric and open-minded, Azuma is rational and detached. He has problems accepting the Brave Police as sapient and is doubtful of Yuuta and his integration into the police by Saejima. However, like Saejima he is competent at his job and worries about any civilian's safety, which expresses in his high demands on the team.
Only Sane Man: For him, the 'miracle' of a machine with A.I. gaining sapience is understandably farstretched to accept, since there is no way to prove it's real. That doesn't even include possible complications nobody knows of yet and could prove disastrous, because the Brave Police are giant robots who are able to lay the city to waste by themselves. You also can't deny he has good reasons to object that Saejima appoints a child in elementary school as the boss to said robots.
Sour Supporter: Despite his objections, he supports the team as much as he can.
Shunsuke Toudou (藤堂・俊助 Toudou Shunsuke), development designer of the Brave Police Japan
Scary Shiny Glasses: They looked like that when Yuuta woke up from a nightmare and saw his father as an obscure figure sitting in the dark and staring at him.
Mother Amami Tomonaga (友永・亜真美 Tomonaga Amami)
Big Eater: She had several dishes in front of her in her debut episode and with the speed she was wolfing down food, she likely had eaten a lot already. But as she says, she has been missing good food abroad.
Robosexual: Ayako's likely more attracted to his personality rather than him being a machine. But they have a mutual love for each other, they go out on dates, and she even kissed him once — although in the latter case, it's merely in Deckerd's dream in episode 40. Then again, considering her character, it'd be likely she would be the one to initiate their first kiss anyway.
Theme Naming: Beatles and Chess - Ringo King, John Bishop, Paul Rook and George Pawn. Playing cards - Ace, Jack and Ten.
(Ringo) King (リンゴ・キング)
Always Someone Better: He always gets compared to Duke and told how much better the other would be. This has made King insecure and doubting himself. He tries to hide this under an arrogant mask and sticking to the rules.
Eye Scream: When one of the Chieftain twins rams his hand through Gaizonite. It survives.
Impaled with Extreme Prejudice: One of the two first Chieftains rams his hand right through its eye from behind as Victim tries to attack Fire J-Decker from behind with Gaizonite's sword form. Gaizonite survives.
Emotion Eater: Inti is an entity that feeds on hidden desires, and by spreading its magic it makes the affected people act out on them. Since such desires are often of violent or dark nature, Inti caused at least one civilisation's demise by its own people destroying their culture.
Off with His Head!: The red Chieftain of the first, original pair was beheaded by Gaizonite in its sword form to prevent him from getting captured by the Brave Police and to transport his Super-A.I. back to Victim O'Rand.
Ironic Name: Many people suffer as victims of his crimes - and he is a victim himself by the crime Neuva committed: he murdered Victim.
Laser-Guided Amnesia: Neuva Fahrzeug killed Victim O'Rand, put a copy of his brain into a Super-A.I. chip, then put the chip into an android disguised as human Victim. On top of that, Neuva made him forget he had shot him and programmed him to do after his bidding unwittingly.