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The first skill that you have to have at least is a good background on mathematics which will help you to understand the robotics modeling and control, then the second important thing is the Matlab which will enable you to simulate and understanding the robot mathematical model which is simply second order differential equations. The above mentioned two issues are already courses given to those graduated specially from Mechanical Engineering, Electrical Engineering and Systems Engineering depts.
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a robotics engineer should have good background on kinematic, mechainical parts and control system. By kinematic knowledge, they can simulate the motion of end effector matematically that useful when they do programming. Knowledge on mechanical part can be help him to select the best part of the manipulator. the last not least in control system skill/knowledge...it will make the robotic engineer be come perfect. he can choose the optimum and the best application for the robot control system..also for the programming language that need to write on the processor.
I think the most important skill for robotics engineer is good understanding of matrix in mathematics and coordinate systems to visualize the movement of robot in real space. Apart from this one should have basic mechanics, electronics and programming knowledge.
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