# Tutorial Review on Space Manipulators for Space Debris Mitigation
## 11 Dual-Manipulator Control
objects (where gravity is exploited). Both require different approaches to grasp planning involving determining the hand pose relative to the target object [263]. The application of a hybrid position/force control selection matrix allows selection of those degrees of freedom which are motion controlled and those which are force controlled in each finger. If force control is dominant, we have a power grasp which is poor at motion control. If motion control is dominant, we have a precision grasp which is poor at rejecting disturbance forces. We may define a grasp performance measure of the form [264]: \(PM=(I-S)^{\gamma}(S)^{1-\gamma}\) where \(\gamma>0.5\) indicates motion-oriented grip and \(\gamma<0.5\) indicates force-oriented grip. Maximisation of the performance measure suggests \(\gamma\to 0.5\) for optimal force stability and motion manipulability. In grasp mechanics, there are three relevant frames of reference: object frame, contact frame and joint frames [265]. The mapping between finger joint torques and the handled object is generally non-linear making it amenable to modelling by artificial neural networks to optimise the contact forces [266]. The grasp matrix defines the kinematic relationship between applied and internal forces at the contact points on the object being handled and those at the centre of mass of the object. There are three types of contact point which define rolling, sliding and sticking contact motion [267]: (i) frictionless (sliding/rolling) contact in which force is exerted only normal to the surface; (ii) frictional (hard) contact based on [PERSON]'s law in which tangential friction force is proportional to normal applied force; (iii) soft contact due to viscoelastic deformation. An object may be grasped at N points of contact: if frictionless, applied forces are normal to the contact point; if frictional, applied forces are both normal and tangential; if a soft contact, a torsional component may be also applied. [PERSON]'s law models friction as \(F_{\parallel}\leq\mu_{\parallel}F_{\perp}\) and \(\tau_{\theta}\leq\mu_{\theta}F_{\perp}\). The contact positions and normals define the grip Jacobian matrix which transforms contact forces into object frame wrenches. There are many different types of end-effector ranging from specialised tools to dual-fingered grippers to multi-fingered hands. While dual fingered jaws may suffice for fixturing workpieces, dextrous manipulation requires multifingered hands with multiple grasp configurations, equilibrium of internal grasping forces, zero slippage, stability of grasp to disturbances and dynamic tactility. The more sides that the polygonal shape possesses (i.e., the closer approximation to circular geometry), the greater the appropriateness for a three fingered grip rather than a two-fingered grip. A three-fingered gripper with three-jointed elastic fingers, a palm joint and soft fingertips allows robust grasping around arbitrary objects, including curling, bending and rotation in three axes [268]. For stability, the three fingertips should have a minimum of three finger contact points. An example is Graspar, a three-fingered gripper capable of grasping complex shapes, adjusting its grasp during slip and yet utilising only a simple binary grasp/release command vocabulary [269]. The two fingers have three joints, while the opposing thumb has two joints, each finger is actuated by a single motorised pair of agonist/antagonist tendons routed over pulleys at the joints and idlers at the centre of each phalange to conform to the object shape. The joints are differentially coupled such that the torque exerted is distributed through the joints according to its moment. Simple contact switches on the grasping surface of each phalange provide simple feedback to ensure simplicity of design and operation yet robust grasping.