MATERIAL Y MÉTODOS El Crucero de Evaluación de

The design of the Hand Arm System is mainly driven by the insight that todays humanoid robot systems are not robust enough to be operated in unstructured environments, where collisions cannot be avoided. This lack of robustness slows down the development of applications in particular us- ing methods that require unsuccessful tasks such as reinforcement learning. Therefore, it seems that

Figure 1.13: Simulation tool for grasp evaluation: GraspIt! future robotic systems have to be able to store energy to meet these requirements [42].

In the recent years a lively discussion about the motivation of variable stiness robots has been led debating their advantages and disadvantages with respect to human interactions and especially safety (e. g. STIFF and THE europeen projects).

In the design of serial elastic actuators the trade-o between robust- ness/mechanical compliance and task performance/mechanical stiness has to be xed. In order to postpone this decision, variable stiness actuators have been proposed [4349]. More recently, a Europeen project VIACTORS was conducted to evaluate the state of the art concerning the variable sti- ness actuators. A valuable output of this project was the denition of a specication datasheet for variable stiness mechanisms (cf. Fig. 1.14).

Using the specication sheets of the mechanisms it is possible to compare, at least globally, the mechanisms. A few of those mechanisms are depicted in Fig. 1.15a, Fig. 1.15b, Fig. 1.15, Fig. 1.16a , and Fig. 1.16b.

Control This section gives an overview of the work done in the last decades in terms of control for nonlinear exible joints. The references are organized in the same order as the control sections.

The use of tendons to actuate the ngers has a number of advantages. However, because tendons can only pull, it is critical to maintain a minimum pulling force on all tendons to avoid issues related to tendon slack. Early work on tendon driven mechanism was introduced in the eld of manipulation [50] and formalized by Kobayashi [19]. He proposed a number of denitions for the properties of tendon driven systems, such as tendon controllability and tendon redundancy. In [51], tendon driven mechanisms are studied with the help of oriented graphs.

More recently, in the context of the development of the Hand Arm Sys- tem, work on the stiness and torque workspace of tendon driven mechanism with nonlinear exible elements was presented in [2]. Similar work on the achievable cartesian stiness of exible joint robot is found in [52]. In [53,54], it is shown that the tendon force distribution problem can be simplied if the

FAS A flexible Antagonistic spring element

Antagonistic finger joint

Operating Data

# (quantity) (unit) (value)

Mechanical

1 Continuous Output Power [W] 67,2 2 Nominal Torque [Nm] 2,2 3 Nominal Speed [rad/s] 16,74 4 Nominal Stiffness

Variation Time

with no load [ms] 29 5 with nominal torque [ms] 29 6 Peak (Maximum) Torque [Nm] 4,9 7 Maximum Speed [rad/s] 152 8 Maximum Stiffness [Nm/rad] 36 9 Minimum Stiffness [Nm/rad] 1,8 10 Maximum Elastic Energy [J] 0,22 11 Maximum Torque Hysteresis [%] 20 12

Maximum deflection with max. stiffness [°] 1,5 13 with min. stiffness [°] 30 14 Active Rotation Angle [°] 150 15 Angular Resolution [''] 3,1 16 Weight [Kg] 3,9

Electrical

17 Nominal Voltage [V] 24 18 Nominal Current [A] 3 19 Maximum Current [A] 7

Control

20 Voltage Supply [V] 24 21 Nominal Current [A] 0,1 22 I/O protocol [] Biss

Spacewire Coaxial Supply

24 V Watercooling tubes

Figure 1.14: Datasheet format created in the VIACTOR project. Example of the tendon mechanism used in the hand of the Hand Arm System (FAS). tendon stiness is linear in the tendon force. In [55], experimental work on the implementation of the tendon force distribution algorithm was reported. In case of small size robots, the friction plays an important role. Un- fortunaly, due to the system size and low serie production, the accurate identication of friction is not a simple task. A complete parameter identi- cation method developed for the LWR (Light-Weight Robot) is presented in [56]. Oine identication methods are time consuming and, often, re- quire assumptions on the friction model [57]. If link side torque sensing is available, it is possible to build an online stiness observer [58]. Moreover, it is shown in [59] that the joint stiness can be estimated online.

When considering exibility in robots, two main branches are considered. Flexible link control, where the links themselves are exing under external loads such as gravity, and exible joint control, where the links are rigid and the joints have a exible behavior. Most of the publications about exible

(a) FSJ (b) FAS

Figure 1.15: VSA-HD.

joint control deal with exibility introduced by the drive train. Consequently, most of the papers are stiness/inertia ratios that are several orders of mag- nitude higher than in the case of the Hand Arm System. When the joint deexion of a robot due to its own weigth is large, the local approximation of the Jacobian are not valid and it becomes challenging to derive global con- trollers [60]. The, usually simple, gravity compensation is not neccessarily simple since the joint stiness needs to fullll new conditions [61, 62] (intu- itively, the stiness should be stronger that the gravity eld). The design of traking controller for exible joint robots has been reported in [63,64]. The application of exible joint control to the active damping of an industrial robot is reported by A. Albu Schäer in [65,66].

Extensive work on the impedance control of redundant exible joint robot has been done by Ott in [67, 68]. Between 1990 and 2000, passivity based control of exible joint system was considered in [69, 70] as well as for a more general class of systems [7173]. Passivity based control is applied to hand control in [74], and to telemanipulation in [72, 75, 76]. Damping control for highly exible robots is considered in [77], where a feedback is used to decouple the dynamics by double diagonalization, compute a proper damping with a pole identication method and apply the controller in the original coordinates.

Impedance control [78] and admittance control [79] have both been ap- plied to tendon control systems. The goal is usually to provide compliance to help in case of inaccuracies in the models or in the sensors. Controllers are used to provide a tendon compliance or to provide a link compliance. In both cases the sensing of the tendon force is required. The Robonaut research group has published serveral papers on the control of the, not an- tagonistically, tendon driven ngers [80, 81]. Control of a joint driven by antagonistic tendon is presented in [82]. Work on the modeling and control of the hand of the University of Bologna is reported in [83].

Several nonlinear control methods have been applied to the control of exible joint control. Examples of such methods are: feedback linearization, Lyapunov redesign, backstepping or sliding mode control. This thesis uses the backstepping method as described in [84, p.489]. In [68,85], the method is applied to exible joint control, however limited to the case of linear stiness and non-antagonistic actuator congurations.

Generally, optimal control method are challenging to implement in real- time, unless closed form solution can be obtained (e. g. optimality of the bang-bang control for some problems [86]). Direct methods to solve the optimal control problem are reported as early as 1960 (cf. [87]). It has been applied to a very large variety of oine optimization problem such as space shuttle trajectory, ship maneuver or throwing problem [88]. How- ever, expected simple cases, the equations can not be solved analytically and do not give any futher insight on the required inputs. Numerical methods are required to construct solutions. Unfortunatly, they require forward and

backward integrations and are generally extremely expensive to compute. An intermediate way between the linear optimal control (Riccati equa- tions) and the optimal nonlinear control (HBJ equations), has been proposed around 1962 by Pearson [89] under the name of State Dependant Riccati Equation (SDRE). It has been expanded by Wernly [90] and popularized by Cloutier [9195]. The method is an intuitive extension of the Algebraic Riccati Equation, applied to a pointwize linearized system. Existance of a SDRE stabilizing feedback is discussed in [96]. The method oers only lim- ited theoretical results for global stability (an excellent survey is provided in [97]) but proved to be eective in practice.