There has been an increase in the number of space missions recently, leading to an increase in space debris. Space debris mainly comprised non-functional spacecraft, abandoned launch vehicles, unburned particles from solid rocket motors, and even paint flecks. Space debris is usually very fast moving and stays in orbit for years or centuries, depending on its trajectory. An extensive simulation proves that Kessler syndrome is already engaged and requires human intervention for lower earth orbit safety. Many space debris capture and removal concepts, such as net capturing, harpoon capturing, ion beam, robotic arm, etc., are proposed. This study proposes a morphing robotic arm to capture space debris. The robotic arm consists of a telescopic type morphing beam so that arm length can be varied. The variation in the arm length increases the debris capture span. Morphing also reduces the arm's weight to span, thus making it flight-worthy. For mathematical modeling, two systems are considered lumped systems and continuous systems for study. The capturing sequence is also divided into instantaneous and probe-cone capturing mechanisms. Post capture vertical motion of robotic arm tip is found out. An Lqr(Linear quadratic regulator) control is implemented to get steady states.