By Seyed Ehsan Shafiei
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Extra info for Advanced Strategies for Robot Manipulators
The global control system In this paper we will use the control of the curve’s shape in each point of the mechanical structure. The method is based on the particular structure of the system defined as a “backbone with two continuous angles θ ( s ) and q(s)”. The control of the system is based on the control of the two angles θ ( s ) and q(s). These angles are measured directly or indirectly. The angle θ ( s ) is measured dircetly by the projection on the image plane ZS1 OS1 YS1 (relation 78) and q(s) is computed from the projection on the image plane ZS2 OS2 YS2 (relation 79).
Korayem M. H. & Nikoobin A. (2009). Optimal Motion Planning of Manipulators with Elastic Links and Joints in Generalized Point-to-Point Task, ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE), Vol. 7, Part B, 33rd Mechanisms and Robotics Conference, pp 1167-1174, San Diego, CA, USA Sentinella M. R. & Casalino L. (2006). , "A unified approach to motion control of mobile manipulators, Int. J. of Robotic Research, Vol. 17, No.
In this case, if we will move the second wire of ΔLw2, we should move the first and third wires with ΔLw2/2 and with the apropiate speed in order to maintain this relation during the movement. Once we know the angle α, we can obtain the value ΔRi = ΔR ⋅ cos (α i ) , defining the displacements of the wires. The algorithm that we are using, assigns the speed of the wires proportional to ΔRi in order to go from the home position (θ =0, α =0) to the position (α, θ)i with a constant speed of the motors.