This story is about 49ers rookie Rashard Robinson, but let’s begin with two other former LSU defensive backs: Patrick Peterson and Tyrann Mathieu.

Three years ago, Peterson vouched for Mathieu, his friend and college teammate, to Arizona general manager Steve Keim and team President Michael Bidwill. Peterson told them Mathieu, who was kicked off the team at LSU after reportedly failing at least 10 drug tests, was a good person who had learned from his missteps.

Mathieu, 24, is now an All-Pro safety and locker-room pillar who signed a five-year, $62.5 million extension Wednesday. Last week, Bidwill said Peterson’s support for Mathieu has made the organization take a harder look at controversial prospects.

“Even if they have been in trouble, we want to look deeper if people are willing to stand up and say, ‘Hey, they’ve learned their lesson,’” Bidwill said. “I think (Peterson) started that.”

This brings us to Robinson, a cornerback who shares striking similarities to Mathieu.

Like Mathieu, he was kicked off the team at LSU, and drug use played a role. Like Mathieu, a Heisman Trophy finalist who fell to the third round, Robinson was projected as an early-round selection but plummeted, lasting until the fourth round. And, like Mathieu, Peterson vouched for Robinson’s character before the draft based on their close connection.

Robinson, 21, and Peterson, 26, are from Pompano Beach, Fla., and attended Blanche Ely High, where the secondary coach is Andrew Wiggins — Robinson’s godfather. Because of their age difference, they weren’t close growing up, but Robinson admired Peterson, who was in his track program, the Pompano Express.

Their relationship deepened when Robinson, a four-star recruit, was a senior and Peterson influenced his decision to sign with LSU. And they’ve become friends and training partners in recent years, with Peterson contacting Robinson when he has returned to Pompano Beach.

Like Mathieu, who lived with Peterson’s parents before he was drafted, Robinson has worked extensively with Peterson’s dad, Patrick Sr., who is an athletic trainer.

Before this year’s draft, the Cardinals again turned to Peterson, a model citizen who is one of four players in NFL history to be named to five Pro Bowls before turning 26. Their question: Is Robinson worth the risk?

“They asked me questions about Rashard as a person because they already knew what type of player he was,” Peterson said. “I definitely told them how it is. He’s a great person and, like I said with Tyrann, that situation doesn’t define him as a man. He was being a college kid that didn’t understand consequences that come with those decisions. I did vouch for him. I did put in their ear that he’s a phenomenal player and a good person.”

Despite Peterson’s pitch, the Cardinals took Texas A&M cornerback Brandon Williams in the third round. The 49ers, who arranged a meeting between Robinson and team pastor Earl Smith in Fort Lauderdale, Fla., a week before the draft, took Robinson with the 133rd pick.

Three months later, the 49ers hope they have Mathieu 2.0. The other possibility, of course, is that they have a player who doesn’t possess the focus, commitment and discipline required to succeed in the NFL.

Those qualities were lacking at LSU, where Robinson, who hasn’t played in a game since Oct. 25, 2014, finished one season during an eight-start career that included two suspensions before he was dismissed.

LSU head coach Les Miles and defensive backs coach Corey Raymond, a former NFL cornerback, have declined to discuss Robinson with The Chronicle through a university spokesman. Mike Detillier, a member of LSU’s radio network who is also a Louisiana-based draft analyst, said Robinson is a “rare talent,” but he finally exhausted the coaching staff’s patience.

“Sometimes you have to hit rock bottom before you understand you aren’t going to be given endless chances in life,” Detillier said. “And I think that was the frustration at LSU. They had given him so many chances — so many opportunities — and he didn’t take advantage of it.”

In 2014, at the start of his sophomore season, Robinson was suspended for the season opener for failing a drug test. After starting six games, he was suspended indefinitely for failing to meet academic requirements.

After missing a semester, Robinson re-enrolled at LSU last year, but was arrested June 12 for unauthorized entry into the apartment of LSU quarterback Anthony Jennings and was dismissed from the team. On Aug. 13, it was determined Robinson wouldn’t be prosecuted because there was “insufficient evidence to obtain a sustainable conviction,” according to a spokeswoman at the East Baton Rouge District Attorney’s Office.

Robinson, who doesn’t have a criminal record, said his arrest was a “big misunderstanding.” He is focused on distancing himself from his mistakes.

“Everything I’ve learned from my past is moving me into the man I am today,” Robinson said. “I’m going to keep doing what I need to do and achieve greatness.”

Those closest to the football-obsessed cornerback believe his banishment from the sport served as his wake-up call.

In the 18 months between his last game at LSU and his draft-day call from the 49ers, Robinson tried to play football, but he didn’t have enough credits to join the team at Broward College in Fort Lauderdale.

What would life be like without the sport? His dad, Reggie Robinson, a cornerback who played four seasons in the Arena Football League, gave him a first-hand look. Reggie, an electrician who is separated from Robinson’s mother, brought Rashard to work with him. Robinson didn’t like being an assistant electrician.

“I knew he didn’t want to come, but I wanted him to see what life was like from my point of view,” Reggie said. “But we had that time to really talk and reflect on some things. … He told me ‘Dad, I’ve got to get with it. I’m going to win in life. I’m going to be a success.’ And so far, he’s held true to his promise. As long as he stays focused, I know he’ll be all right.”

Reggie said he’s given his son tough-love counsel. And Rashard received more from Patrick Peterson Sr., who didn’t allow his own son to play football as a high school sophomore because of poor grades.

Robinson, who worked with Peterson Sr. before the combine in February, quickly learned to not to arrive late to training sessions. His punishment included extra running, push-ups and animated conversation with Peterson Sr.

“It was just being in Rashard’s ear a little bit,” Peterson Sr. said. “It was just sort of embarrassing him a little bit just to help him understand: ‘You’re going into a man’s world now. There’s going to be a lot of that, so get used to it.’ I wanted to make sure he understood: There can’t be any more screwups.”

Patrick Sr., like his All-Pro son, has invested in Robinson because he doesn’t want him to squander his elite ability. Niners defensive coordinator Jim O’Neil said Robinson (6-foot-1, 177 pounds) displayed some of the best press-coverage techniques he has seen in a college player when he was at LSU.

Detillier said Robinson’s only full college season was jaw-dropping. Because of questions about his academic standing, Robinson missed preseason practice and the first week of school as a freshman. Still, he played 12 games, made two starts and was named the SEC co-Freshman of the Week after limiting Texas A&M’s Mike Evans, the No. 7 pick in 2014, to four catches for 51 yards.

“This is a guy who came in a few days before the regular season and started two games as a true freshman,” Detillier said. “There are not a lot of guys who have that on the resume. Partner, all I can tell you is, that’s pretty doggone good.”

With the 49ers, Robinson has earned rave reviews for his feisty and fearless play during offseason practices and training camp. Off the field, head coach Chip Kelly said Robinson has been “all about football,” and O’Neil said there has been no whiff of character problems.

After a recent practice, Robinson, who trained with Mathieu before the 2013 draft, was told the Cardinals’ safety had signed his $62.5 million extension.

“Really?” he responded. “Wow, that’s my guy.”

Three years after the Cardinals’ risky pick paid off, the 49ers hope Mathieu is the guy Robinson will emulate in the NFL.

Eric Branch is a San Francisco Chronicle staff writer. Email: ebranch@sfchronicle.com Twitter: @Eric_Branch