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Kinematic Control of a New Hyper-Redundant Manipulator with Lockable Joints

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Kinematic Control of a New Hyper-Redundant Manipulator with Lockable Joints Scientia Iranica B (2013) 20(6), 1742{1752 Sharif University of Technology Scientia Iranica Transactions B: Mechanical Engineering www.scientiairanica.com Kinematic control of a new hyper-redundant manipulator with lockable joints A. Taherifar, H. Salarieh and A. Alasty Center of Excellence in Design, Robotics and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Tehran, P.O. Box 11155-9567, Iran. Received 8 June 2012; received in revised form 20 April 2013; accepted 25 June 2013 KEYWORDS Abstract. Kinematic control of a special hyper-redundant manipulator with lockable joints is studied. In this manipulator, the extra cables are replaced by a locking system Redundant to reduce the weight of the structure and the number of actuators. This manipulator has manipulator; discrete and continuous variables due to its locking system. Therefore, a hybrid approach Kinematic control; has been adopted in control. At rst the forward kinematics and velocity kinematics of this Lockable joints; manipulator are derived, and then a novel closed-loop control algorithm is presented. This Tendon-actuated algorithm consists of decision making, an inner loop controller, and kinematic calculation manipulator. blocks. The decision making block is the logical part of the control scheme in which suitable switches will be chosen. The control block uses the end-e ector position feedback to generate appropriate commands. The performance of the proposed hybrid control scheme in position tracking is assessed for several trajectories. © 2013 Sharif University of Technology. All rights reserved. 1. Introduction RT1 in which all of the DOFs are actuated by only one motor via especially designed hinge bar universal Kinematically redundant manipulators have more De- joints; as a result, the manipulator weight is greatly grees Of Freedom (DOF) than required for determining reduced. Ananiev et al. [6] also designed a single-motor the position and orientation of the end-e ector [1]. driven construction of a hyper-redundant robot using Due to their high exibility, they have a great po- the same method used in [5], but, instead of hinge bar tential to work in fully constrained, complex and universal joints, they used exible shafts. Todd and hazardous environments, such as nuclear reactors and Drozda [7,8] developed a tendon-actuated robot, and space stations [2]. They can also be used for surgery, put all of the actuators out of the manipulator in order exploration, and rescue. to decrease the weight of the robot. In the past two decades, many redundant ma- Hirose and Ma [9] implemented a coupled tendon nipulators with various structures and di erent types driven manipulator with a speci c tendon traction force of actuation have been proposed. Actuation with mechanism in which a pair of tendons is pulled by base cables is one common type of manipulator operation, actuators via pulleys mounted on the base-side joint. which is called tendon-actuation [3]. Some other Kimura and [10] designed a 15-DOF manipulator, manipulators [4] use pneumatic actuators. Li et al. [5] which has 7 joint modules and one prismatic joint designed a novel hyper redundant manipulator, named on the bottom; each joint module has 2 actuators. Chirikjian and Burdick [11] developed a 30-DOF robot consisting of 10 identical 3-DOF truss modules. Sham- *. Corresponding author. Tel.: +98 21 66165538 E-mail addresses: [email protected] (A. Taherifar); mas et al. [12] designed a new 3-DOF joint for snake- [email protected] (H. Salarieh); [email protected] (A. like robots using an angular bevel gear train. Jones Alasty) et al. [13] designed a novel continuum manipulator. A. Taherifar et al./Scientia Iranica, Transactions B: Mechanical Engineering 20 (2013) 1742{1752 1743 The design features two concentric exible cylinders, with a pneumatically actuated inner tube and tendons xed to an outer cylinder. Ning et al. [14-16] built a new 3-D modular hyper-redundant manipulator. All the joints of this manipulator are passive and state controllable and share a common input introduced by wire-driven control. The trajectory planning of redundant manipulators is also an important area of research. Marcos et al. [17] studied the trajectory planning of such manipulators using the genetic algo- rithm. A novel, tendon-actuated, hyper redundant ma- nipulator was introduced by Honorary [18] in 2009. The novelty of this tendon-actuated manipulator is due to the use of a locking mechanism in the joints, which makes it controllable with only three cables. Therefore, by releasing and locking the joints in an arbitrary sequence and by stretching the cables, the con gura- tion of the manipulator changes. This mechanism of actuation has discrete and continuous variables, which Figure 2. The schematic of the cable-actuated hyper makes the control problem sophisticated. In this paper, redundant manipulator. The ith link is unlocked and the the modeling and kinematic control of this manipulator others are locked. are studied. In order to have a deep understanding of the and reduce the total weight and cost. An eight- control scheme presented in the following sections, it is DOF prototype has been designed and made at Sharif essential to give a brief description of the manipulator. University for practical experiments. Shafaei [19] opti- Each module of the manipulator (links and joints) mized and utilized the manipulator in 2011. Although consists of three hydraulic jacks, which are arranged in the structure of the manipulator is simpli ed by this a parallel con guration (3RPS (3-Revolute-Prismatic- novel idea, the path planning and control problem Spherical)). The lengths of these jacks are either xed are enormously complicated. Taherifar et al. [20] has (locked) or varying (unlocked) due to the solenoid studied the path planning of the planar manipulator us- state. The solenoid valves are the main components of ing the Particle Swarm Optimization (PSO) technique. the locking mechanism which are put in the hydraulic In [20], inverse kinematics is solved with continuous circuit, as shown in Figure 1. Once they are chosen to PSO and the sequence of switching is optimized with be unlocked, the length of the jacks can be controlled the discrete PSO algorithm. The minimum time and by the wires. minimum switch path planning of this manipulator are Actuators are three cables which pass through also studied in [21]. The minimum switch path will joints all along the arm, as shown in Figure 2. When decrease vibration and energy consumption. a link is locked, the position and orientation of that In previous designs of this category, one set of link remains unchanged. At any time, all links of cables was used to control the orientation of each joint. the manipulator are locked except one. Whenever the For example, to control a joint with two degrees of cables are moved, the manipulator will tilt to its new freedom, at least 3 cables were needed. So, if the position while all other locked links move as a rigid manipulator has 4 joints, there should be at least body. Lockable joints decrease the number of actuators 12 cables to control the arm. In this design, a lock mechanism in each joint is used to lock all degrees of freedom except 2 degrees, which can be controlled by 3 cables extended along the whole arm. Pulling the cables will create torque along the arm. By choosing which lock to be opened, the torque created by the cables will change the orientation of that joint. In this paper, the modeling and control of the robot have been investigated. The 3RPS mechanism has 3 degrees of freedom (Figure 3). In addition, the hydraulic circuit shown Figure 1. The hydraulic circuit of locking system in each in this gure adds a constraint to the mechanism that link. reduces one degree of freedom when all solenoid valves 1744 A. Taherifar et al./Scientia Iranica, Transactions B: Mechanical Engineering 20 (2013) 1742{1752 According to Figure 3, the position vector of the upper end of the limbs, B1, B2 and B3 can be written as: 2 3 2 3 2 3 x1 x2 x3 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 B1 = 6y17 ;B2 = 6y2 7 ;B3 = 6y3 7 : (3) 4 5 4 5 4 5 z1 z2 z3 The distance between the upper ends of the adjacent limbs is constant in any con guration, that is: 8 2 2 2 2 <>(x1 x2) + (y1 y2) + (z1 z2) = d2 (x x )2 + (y y )2 + (z z )2 = d2 ; (4) > 1 3 1 3 1 3 2 : 2 2 2 2 (x2 x3) + (y2 y3) + (z2 z3) = d2 where d2 is the upper platform length. Now, xi and yi in Eq. (4) are substituted in terms of l , l , l and , Figure 3. Schematic of the link mechanism for the 1 2 3 1 redundant manipulator with RPS mechanism. 2, 3. Finally, the kinematic equations of a link are deriven: are open, that is: p p 8 2 >d1 3d1l1 cos(1) 3d1l2 cos(2) > 2 l + l + l = const; (1) > + l1l2 cos(1) cos(2) + l 1 2 3 > 1 > 2l l sin( ) sin( ) + l2 = d2 > 1 2 1 2 2 2 where l , l and l are the lengths of the jacks. When > 1 2 3 > solenoid valves are closed, the mechanism is completely > p p > 2 locked. <d1 3d1l1 cos(1) 3d1l3 cos(3) 2 In the next section, the forward kinematics and + l1l3 cos(1) cos(3) + l1 (5) > 2 2 > 2l1l3 sin(1) sin(3) + l = d velocity kinematics of this manipulator are derived. > 3 2 > A closed loop control scheme is proposed for the > > p p hyper-redundant manipulator with lockable joints in >d2 3d l cos( ) 3d l cos( ) > 1 1 2 2 1 3 3 Section 3.
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