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The Fukushima power station in Japan was affected by a major earthquake and tsunami in March 2011, inspecting the primary containment vessel remains difficult due to high radioactivity. Long-reach robot arms are useful in inspecting such hazardous environments, and a coupled tendon-driven mechanism enables realizing a long, light-weight, and thin manipulator. However, high elastic elongation of tendons due to gravity may lead to unstable joint control. In this paper, we introduce dynamics-based control as a feasible strategy for a long-reach tendon-driven robotic arm. Additionally, a planning method to identify the joint angle path ensuring stability is proposed. Considering stability analysis, the potential due to the tendon elasticity and gravity is evaluated and used as an index of joint stability. The rapidly exploring random tree is used as the planning algorithm. The effectiveness of the proposed method was demonstrated through the successful manipulation of a 5-kg payload by a 10-m long robotic arm. [ABSTRACT FROM AUTHOR]