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Joint Torque sensory Feedback (JTF) can substantially improve the performance of a robotic system. JTF makes it possible to achieve dynamic control of a robotic manipulator without the need for modeling its link dynamics. Moreover, it has been proved that JTF can achieve a precise torque tracking in a manipulator joint by compensating the e ect of joint friction and actuator nonlinearities. Despite these advantages, accurate joint torque measurement encounters several practical challenges. Since much of the torque/force reaction of the link load on the joints appears in the form of nontorsional components, e.g. overhung force and bending moment, the torque sensing device has to not only bear but remain insensitive to these force/moment components. In addition, it is desirable to design the structure of the sensor such that it generates a large strain for a given load torque and therefore has a high sensitivity. However, this is in conflict with the high-sti ness requirement for minimizing the joint angle error introduced by the sensor. The main objectives of this chapter are twofold: Firstly, in Sections 2 and 3, we describe the technical challenges and practical solutions to accurate measurement of joint torques in the presence of the non-torsional components in a robot joint. For a torque sensing device, di erent mechanical structures will be examined and their properties, such as sensitivity and sti ness in di erent directions and decoupling, will be explored. This allows a systematic design of a sensor structure which is suitable for torque measurement in a robot joint. Finally, the state-of-the-art and design of a torque sensor for robots will be presented in Section 4. The design achieves the conflicting requirements of high sti ness for all six force and torque components, high sensitivity for the one driving torque of interest, yet very low sensitivity for the other five force/torque components. These properties, combined with its donut shape and small size make this sensor an ideal choice for direct drive robotic applications. Experimental data validates the basic design ideas underlying the sensor’s geometry, the finite element model utilized in its optimization, and the advertised performance. The second objective is to describe the application of joint torque sensory feedback (JTF)in robot control. The main advantages claimed for JTF are (i) it can simplify the complexity of the system dynamics by eliminating its link dynamics; and (ii) the control system is inherently robust with respect to both external force disturbance and parameter variation. First, assuming both actuator and torque sensor are ideal, we describe robot control with JTF in Section 5. Then, development of an adaptive JTF is presented in Section 6that requires only the incorporation of uncalibrated joint torque signals, i.e., the gains and o sets of multiple sensors are unknown. Also, all physical parameters of the joints including inertia of the rotors, link twist angles, and friction parameters are assumed unknown to the

Multi-body systems’ (MBS) dynamics are often described by the second-order nonlinear equations parameterized by a configuration-dependent inertia matrix and the nonlinear vector containing the Coriolis and centrifugal terms. Since these equations are the cornerstone for simulation and control of robotic manipulators, many researchers have attempted to develop efficient modelling techniques to derive the equations of motion of multi-body systems in novel forms. A unifying idea for most modeling techniques is to describe the equations of motion in terms of general coordinates and their time–derivatives. In classical mechanics of constrained systems, a generalized velocity is taken to be an element of tangential space of configuration manifold, and a generalized force is taken to be the cotangent space. However, neither does space possess a natural metric as the generalized coordinates or the constrains may have a combination of rotational and translational components. As a result, the corresponding dynamic formulation in not invariant and a solution depends on measure units or a weighting matrix selected Aghili (2005); Angeles (2003); Lipkin and Duffy (1988); Luca and Manes (1994); Manes (1992). There also exist other techniques to describe the equations of motion in terms of quasi–velocities, i.e., a vector whose Euclidean norm is proportional to the square root of the system’s kinetic energy, which can lead to simplification of these equations Aghili (2008; 2007); Bedrossian (1992); Gu (2000); Gu and Loh (1987); Herman (2005); Herman and Kozlowski (2006); Jain and Rodriguez (1995); Junkins and Schaub (1997); Kodischeck (1985); Kozlowski (1998); Loduha and Ravani (1995); Papastavridis (1998); Rodriguez and Kertutz-Delgado (1992); Sinclair et al. (2006); Spong (1992). A recent survey on some of these techniques can be found in Herman and Kozlowski (2006). In short, the square–root factorization of mass matrix is used as a transformation to obtain the quasi–velocities, which are a linear combination of the velocity and the generalized coordinates Herman and Kozlowski (2006); Papastavridis (1998). It was shown by Kodistchek Kodischeck (1985) that if the square–root factorization of the inertia matrix is integrable, then the robot dynamics can be significantly simplified. In such a case, transforming the generalized coordinates to quasi–coordinates by making use of the integrable factorization modifies the robot dynamics to a system of double integrator. Then, the cumbersome derivation of the Coriolis and centrifugal terms is not required. It was later realized by Gu et al. Gu and Loh (1987) that such a transformation is a canonical transformation because it satisfies Hamilton’s equations. Rather than deriving the mass matrix of MBS first and then obtaining its factorization, Rodriguez et al. Rodriguez and Kertutz-Delgado (1992)