4 Human.Inspired Hyper Dynamic Manipulation

Hyper dynamic manipulation is defined as highly skilled manipulation with hyper motion specifications, as performed by some athletes. Though hyper dynamic manipulation has been realized in some conventional robots, how to realize hyper dynamic manipulation by a smart structure still remains an interesting and challenging topic to be studied in the robotics field. The purpose of this work is to realize human-inspired hyper dynamic manipulations by a smart manipulator. Based on the analysis results from human hyper dynamic motion, we propose a solution to the realization of hyper dynamic manipulation by robots through utilizing dynamically coupled driving and structural joint stops. This chapter gives the basic idea for utilizing dynamically coupled driving and structural joint stops in a hyper dynamic manipulator The implementation method shows how to realize the manipulation, and the simulations and experimental results provide verification of the overall effectiveness of this proposal.

4.1 Introduction

Hyper dynamic manipulation is defined here as highly skilled manipulation with hyper motion specifications, as performed by some athletes. Realization of such hyper dynamic manipulation by a robot is an interesting and challenging topic in robotics, because the need for the capability of dynamic manipulation is increasing

Although some robots have been developed to perform hyper dynamic manipulation, these robots conform to the conventional robot design method, that of designing the robot by satisfying the specifications of velocity and acceleration of individual joints (Shimon 1999).

The revolute joint of a manipulator usually cannot rotate 360 degrees due to the structural limitation The rotation range of the joint is limited by a mechanical structure, namely, the joint stop Conventional manipulators provide protection against collision or contact between an arm and the joint stop by employing a software barrier based on the rotation range of each joint and an electronic hardware barrier using a proximity sensor and a control circuit That is, the passive torque between the joint stop and the arm is not utilized by conventional manipulators.

Recent advances in the mechanical design of manipulators have produced a new generation of lightweight manipulators (Hirzinger et al. 2001). Such work focused on how to design compact mechanisms for a manipulator The research and development on manipulators has provided the foundation for work on humanoids (Kagami et al. 2001). Though humanoids can do some dynamic manipulations, such as some kinds of slow dancing and running (Nagasaka et al 2004), they are still limited in their dynamic manipulation capability due to conventional robot design methods.

Compared to conventional manipulators, human beings can perform hyper dynamic manipulations while in a smart structure The motion control skill, namely, efficiently utilizing dynamically coupled driving in hyper dynamic manipulation, has been presented in previous work (Ming et al 2001) That successful motion is due to the smart structure of humans, in which the joints near the body are more powerful than those near the end of the arm To produce a hyper dynamic action, the power of the joint near the body must be transferred to the parts near the palm by multistep acceleration due to dynamically coupled driving In addition, a human's arthrosis cannot rotate all around like conventional manipulators due to limitations of the body's structure (joint stop). Such limitations are often utilized by humans to improve their capability of dynamic manipulation For example, in the downswing phase of a high-speed golf swing motion, the joint stop in the wrist joint is utilized by professional golfers to accelerate the golf club (Ming, Kajitani, and Shimojo 2002; Ming et al. 2001; Ming et al. 2003).

As a human-inspired approach to improve the capability of a manipulator for hyper dynamic manipulations by a smart structure, we propose to utilize dynamically coupled driving and the joint stop in the manipulator That is, to make the joint stop in the manipulator available and utilize the structural joint stops effectively by a unique control method based on dynamically coupled driving This will lead to a large improvement on the dynamic capability.

This chapter gives the basic idea and expected effects of utilizing dynamically coupled driving and structural joint stops in a manipulator in Section 4.2 The control method to utilize dynamically coupled driving and joint stops is described in Section 4.3 Simulation and experimental results and discussion are given in Section 4.4 Section 4.5 concludes.

4.2 Basic Concept

4.2.1 Utilization of Dynamically Coupled Driving

As mentioned before, humans can utilize dynamically coupled driving while performing hyper dynamic manipulation, which provides a useful suggestion of realizing hyper dynamic manipulation by a manipulator with a smart structure There have been some works about the positioning control of manipulators with passive joints using dynamically coupled driving (Arai and Tachi 1991; DeLuca and Oriolo 2002; Nakamura, Koinuma, and Suzuki 1996) Here, we consider how to utilize dynamically coupled driving to design a hyper dynamic manipulator with a smart structure.

For a planar n-degrees-of-freedom (DOF) open-chained multijoint manipulator, the dynamics equation is (Murry, Li, and Sastry 1994):

$τ = M (Θ) \overset{..}{Θ} + C (Θ, \dot{Θ}) \dot{Θ} + N (Θ, \dot{Θ})$ $τ = M (Θ) \overset{..}{Θ} + C (Θ, \dot{Θ}) \dot{Θ} + N (Θ, \dot{Θ})$ (4.1)

where

θ = generalized driving torque

θ = generalized coordinate

M(θ) = inertia matrix

C (θ,⊙) = Coriolis matrix determining the Coriolis force and the centrifugal force

N (θ,⊙) = gravity force and frictional/damping force

The scalar form of the equation is as follows:

${. . ... n ... \cdot n = . 1 = 1 n . n ... n M_{1} . \cdot (Θ) {\overset{..}{Θ}}_{i} . + M_{ni} (. Θ Θ) {\overset{..}{Θ}}_{i} + \cdot \sum_{k = 1}^{i^{k}} . Γ_{i^{k}} n . . {\dot{Θ}}_{i} {\dot{Θ}}_{k} + \cdot N_{n} (. Θ, \dot{Θ}) l . . \cdot . . \cdot \cdot ... \cdot . \cdot$ ${. . ... n ... \cdot n = . 1 = 1 n . n ... n M_{1} . \cdot (Θ) {\overset{..}{Θ}}_{i} . + M_{ni} (. Θ Θ) {\overset{..}{Θ}}_{i} + \cdot \sum_{k = 1}^{i^{k}} . Γ_{i^{k}} n . . {\dot{Θ}}_{i} {\dot{Θ}}_{k} + \cdot N_{n} (. Θ, \dot{Θ}) l . . \cdot . . \cdot \cdot ... \cdot . \cdot$ (4.2)

where

$Γ_{ijk} = \frac{1}{2} {\frac{\partial M_{ij} (Θ)}{\partial Θ_{k}} + \frac{\partial M_{ik} (Θ)}{\partial Θ_{j}} - \frac{\partial M_{kj} (Θ)}{\partial Θ_{i}}}$ $Γ_{ijk} = \frac{1}{2} {\frac{\partial M_{ij} (Θ)}{\partial Θ_{k}} + \frac{\partial M_{ik} (Θ)}{\partial Θ_{j}} - \frac{\partial M_{kj} (Θ)}{\partial Θ_{i}}}$ $C_{i} i (Θ, \dot{Θ}) = \sum_{k = 1}^{n} Γ_{i} {\dot{Θ}}_{k} i^{k}$ $C_{i} i (Θ, \dot{Θ}) = \sum_{k = 1}^{n} Γ_{i} {\dot{Θ}}_{k} i^{k}$

Obviously, there are dynamic coupling relations among the different equations of the set in Equation (4.2) To analyze these relations more clearly, we subtract t_i+1 from T_i (i = 1,—, n - 1) and write it in the world coordinate frame, resulting in the following equation:

$τ_{i} - τ_{i + 1} + τ_{id} = (J_{i} + m_{i} l_{gi}^{2} + l_{i}^{2} \sum_{j = i + 1}^{n} m_{j}) {\overset{..}{Φ}}_{i} + (m_{i} l_{gi} + l_{i} \sum_{j = i + 1}^{n} m_{j}) gcos Φ_{i}$ $τ_{i} - τ_{i + 1} + τ_{id} = (J_{i} + m_{i} l_{gi}^{2} + l_{i}^{2} \sum_{j = i + 1}^{n} m_{j}) {\overset{..}{Φ}}_{i} + (m_{i} l_{gi} + l_{i} \sum_{j = i + 1}^{n} m_{j}) gcos Φ_{i}$ (4.3)

where

$τ_{id} = - \sum_{j = 1, j \neq i}^{n - 1} P_{j} (M, L, L_{g}) [{\overset{..}{Φ}}_{j} cos (Φ_{i} - Φ_{j}) + {\dot{Φ}}_{j}^{2} sin (Φ_{i} - Φ_{j})]$ $τ_{id} = - \sum_{j = 1, j \neq i}^{n - 1} P_{j} (M, L, L_{g}) [{\overset{..}{Φ}}_{j} cos (Φ_{i} - Φ_{j}) + {\dot{Φ}}_{j}^{2} sin (Φ_{i} - Φ_{j})]$

Ji is the moment of inertia of link i about the center of mass, m_{ is the mass of link i, l. is the length of link i, is the length from the centroid to joint of link i, cp_i is the angular position of link i referring to the world coordinate, Pj (m, l, lg ) is the coefficient function, and g is acceleration due to gravity. In particular, for the end-effector the following equation holds:

$τ_{n} + τ_{nd} = (J_{n} + m_{n} l_{gn}^{2}) {\overset{..}{Φ}}_{n} + m_{n} g l_{gn} cos Φ_{n}$ $τ_{n} + τ_{nd} = (J_{n} + m_{n} l_{gn}^{2}) {\overset{..}{Φ}}_{n} + m_{n} g l_{gn} cos Φ_{n}$ (4.4)

where

$τ_{nd} = - m_{n} l_{gn} \sum_{j = 1}^{n - 1} {\overset{..}{Φ}}_{j} l_{j} cos (Φ_{n} - Φ_{j}) + {\dot{Φ}}_{i}^{2} l_{j} sin (Φ_{n} - Φ_{j})$ $τ_{nd} = - m_{n} l_{gn} \sum_{j = 1}^{n - 1} {\overset{..}{Φ}}_{j} l_{j} cos (Φ_{n} - Φ_{j}) + {\dot{Φ}}_{i}^{2} l_{j} sin (Φ_{n} - Φ_{j})$

It is very clear that both terms on the right-hand side of Equations (4.3) and (4.4) represent the motion equation of a single pendulum. According to this characteristic, the multi-joint manipulator can be regarded as a dynamic system consisting of single pendulums connected serially. The whole motion of the manipulator is the compound motion of the single pendulums. On the other hand, according to the terms on the left-hand side of Equations (4.3) and (4.4), all of the links are driven by not only the active torque from the actuators but also the torque x_id due to coupling. We call this dynamically coupled driving torque.

Therefore, due to the existence of dynamically coupled driving in a planar open-chained manipulator, we hope to utilize it to improve the capability of hyper dynamic manipulation of a manipulator. Further, if there are nonper-pendicular joints in a spatial manipulator, there is still dynamically coupled driving torque among these joints Thus, it can be utilized as such in a planar manipulator.

As an example, we discuss a simplified two-joint manipulator shown in Figure 4.1 in detail. According to Equations (4.3) and (4.4), its dynamics can be written as:

$τ_{1} - τ_{2} + τ_{1 d} = (m_{1} l_{21}^{2} + m_{2} l_{1}^{2} + J_{1}) {\overset{..}{Φ}}_{1} + (m_{1} g_{y} l_{g 1} + m_{2} g_{y} l_{1}) cos Φ_{1}$ $τ_{1} - τ_{2} + τ_{1 d} = (m_{1} l_{21}^{2} + m_{2} l_{1}^{2} + J_{1}) {\overset{..}{Φ}}_{1} + (m_{1} g_{y} l_{g 1} + m_{2} g_{y} l_{1}) cos Φ_{1}$ (4.5)

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FIGURE 4.1

Model of a two-joint manipulator.

$τ_{2} - 0 + τ_{2 d} = (m_{2} l_{22}^{2} + J_{2}) {\overset{..}{Φ}}_{2} + m_{2} g_{y} l_{g 2} cos Φ_{2}$ $τ_{2} - 0 + τ_{2 d} = (m_{2} l_{22}^{2} + J_{2}) {\overset{..}{Φ}}_{2} + m_{2} g_{y} l_{g 2} cos Φ_{2}$ (4.6)

where

$τ_{1 d} = m_{2} l_{1} l_{g 2} ({\overset{..}{Φ}}_{2} cos β_{21} - {\dot{Φ}}_{2}^{2} sin β_{21})$ $τ_{1 d} = m_{2} l_{1} l_{g 2} ({\overset{..}{Φ}}_{2} cos β_{21} - {\dot{Φ}}_{2}^{2} sin β_{21})$

$τ_{2 d} = m_{2} l_{1} l_{g 2} ({\overset{..}{Φ}}_{1} cos β_{21} + {\dot{Φ}}_{1}^{2} sin β_{21})$ $τ_{2 d} = m_{2} l_{1} l_{g 2} ({\overset{..}{Φ}}_{1} cos β_{21} + {\dot{Φ}}_{1}^{2} sin β_{21})$

θ ! = θj and ç₂ = 8x + 8₂, which represent the angular positions of joints 1 and 2 in their world coordinates, and ß_2X = 8₂ - n represents the angular position of link 2 relative to link 1. ^Tid/ ^T2d are dynamically coupled driving torques. t-2<¿ consists of two parts:

$τ_{2 d} = τ_{2 dv} + τ_{2 da}$ $τ_{2 d} = τ_{2 dv} + τ_{2 da}$ (4.7)

where:

$τ_{2 dv} = m_{2} l_{1} l_{g 2} {\dot{Φ}}_{1}^{2} sin β_{21}$ $τ_{2 dv} = m_{2} l_{1} l_{g 2} {\dot{Φ}}_{1}^{2} sin β_{21}$

$τ_{2 da} = m_{2} l_{1} l_{g 2} {\overset{..}{Φ}}_{1} cos β_{21}$ $τ_{2 da} = m_{2} l_{1} l_{g 2} {\overset{..}{Φ}}_{1} cos β_{21}$

We define t2dv as velocity coupling torque and T_2da as acceleration coupling torque The velocity coupling torque is always positive and helps the active torque to accelerate joint 2 should the relative angular position ß₂₁ e [0,rc]. The acceleration coupling torque is rather complex and is determined by both acceleration of joint 1 cp 1 and relative angular position ß₂i. Only if both <ip ₁ and cos ß₂₁ are positive or negative does t_2da contribute to the acceleration of joint 2. Figure 4.2 shows the effect of dynamically coupled driving torque in joint 2. The "+" represents an acceleration effect and "-" represents a deceleration effect.

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FIGURE 4.2

Effect of dynamically coupled driving torque in joint 2.

In accordance with Equation (4.7) and Figure 4.2, we can utilize the dynamically coupled driving torque to accelerate joint 2. However, to accelerate joint 2, joint 1 must accelerate first to a very high angular velocity; that is, it must obtain a large velocity coupling torque and acceleration coupling torque when link 2 is in quadrant I ( ß₂₁ e [0, rc/ 2]). But, when link 2 is in quadrant II ( ß₂i e [V2, n]), joint 1 must decelerate in order to maintain the acceleration effect of the acceleration coupling torque in joint 2.

Utilizing the same analysis method, we can define:

$τ_{1 d} = τ_{1 dv} + τ_{1 da}$ $τ_{1 d} = τ_{1 dv} + τ_{1 da}$ (4.8)

where

$τ_{1 dv} = - m_{2} l_{1} l_{g 2} {\dot{Φ}}_{2}^{2} sin β_{21}$ $τ_{1 dv} = - m_{2} l_{1} l_{g 2} {\dot{Φ}}_{2}^{2} sin β_{21}$

$τ_{1 da} = m_{2} l_{1} l_{g 2} {\overset{..}{Φ}}_{2} cos β_{21}$ $τ_{1 da} = m_{2} l_{1} l_{g 2} {\overset{..}{Φ}}_{2} cos β_{21}$

The effect of dynamically coupled driving torque in joint 1 is shown in Figure 4.3.

By comparing Figures 4.2 and 4.3, we conclude that (1) the effects of velocity coupling torque on joint 1 and joint 2 are opposite at any position; and (2) the acceleration of joint 2 results in the same acceleration effect on joint 1 in quadrants I and IV but results in the opposite deceleration effect on joint 1 in quadrants II and III Therefore, to utilize the dynamically coupled driving to accelerate joint 2, the deceleration effect on joint 1 is inevitable in quadrant II

Actually, the effect of dynamically coupled driving is due to the power transfer from joint 1 to joint 2 by multistep acceleration Because it is possible to use the dynamically coupled driving torque instead of the active torque as the main driving torque, a light, low-power actuator can be used near the end-effector (joint 2) to lighten the structural weight of a manipulator This benefits the dynamic manipulation. On the other hand, a more powerful actuator can be used on the base (joint 1) to overcome the deceleration effect of the dynamically coupled driving torque resulting from joint 2; that is, to supply more power to joint 1 so that more power will be transferred to joint 2 In so doing, the capability of dynamic manipulation is improved

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FIGURE 4.3

Effect of dynamically coupled driving torque in joint 1.

Similarly, due to the existence of dynamically coupled driving in an n-DOF open-chained manipulator, it is possible to utilize it to improve the capability of dynamic manipulation of the whole manipulator According to the analysis of the two-link model, dynamically coupled driving torque, rather than active torque, can be utilized to drive joints of an n-DOF manipulator. Hence, all of the joints except the one on the base are driven by lighter, low-power actuators compared to those of conventional manipulators Further, the actuator in joint i can be selected so that its load capability is only a little greater than the static torque due to the weight of the mechanism from link i to the end-effector To supply power to be transferred to the end-effector, a more powerful actuator is selected and mounted on the base to drive the first link. By selecting lighter, low-power actuators, the links can also become lighter Then the weight of such a structure is significantly lighter than that of conventional manipulators, and it is beneficial to the improvement of the capability of dynamic manipulation Only one high-power actuator is required to realize hyper dynamic manipulation

Because of the utilization of low-power actuators, the active torque is strictly limited It is necessary to develop a method to utilize dynamically coupled driving to improve the capability of hyper dynamic manipulation of a manipulator subject to such active torque limitation According to Equations (4.3) and (4.4) and the discussion above, the dynamically coupled driving torque is determined by the motion states of manipulators One rational way to utilize dynamically coupled driving is planning a special motion trajectory that can utilize it effectively during the whole motion phase However, the complicated relation between the effect of dynamically coupled driving and the motion states and the strict active torque limitation make it difficult to find such a motion trajectory directly. We deal with this problem by adopting an optimization method The trajectory of hyper dynamic manipulation is generated subject to the active torque limitation and motion equation. If the motion can be generated under this condition, then dynamically coupled driving is to be utilized to drive the manipulator in the motion rather than the active torque

4.2.2 Utilization of Structural Joint Stop

The other key point for human hyper dynamic manipulation is the structural joint stop utilized by humans. Much work has already been done investigating the elastic and damping characteristics of the joint stop. Some work (Hogan 1985) has focused on realizing the desired compliance by controlling the joint actuators, whereas others (Hayakawa et al. 1996; Katsurashima et al. 1998; Laurin-Kovitz, Colgate, and Carnes 1991; Mizuuchi et al. 1998; Morita et al. 1998; Okada, Nakamura, and Ban 2001) tried to utilize special mechanisms in order to meet the compliance requirements. All of the work previously mentioned is based on an assumption that the load is within the load capability of all actuators in the joints.

Our proposal is different We propose the passive elastic and damping characteristics of the structural joint stop within the stop positions of the joint to be utilized to improve the capability of dynamic manipulation of manipulators, in addition to the elastic and damping characteristics realized by controlling the actuators or supplied by some mechanisms within the rotation range of a joint.

The reasons for using the structural joint stop in a manipulator are as follows:

• Large load capability: The load capability of a mechanical joint stop depends on its structural strength, instead of the load capability of an actuator This will be useful to transfer high power from the joints near the base to the joints near the end of the manipulator

• Easy realization by simple and compact mechanism: The structure of the joint stop can be built into the joint as a simple module, instead of a conventional stiff joint stop

• Power savings: The configuration of a manipulator, in which some or all joints are in joint stop positions, can be used as a rest configuration By switching off the servo loops of the joints in joint stop positions, power savings is possible

Therefore, it is possible to realize efficient dynamic manipulations by utilizing the joint stop, compared to conventional manipulators limited by the load capability of actuators.

Considering the utilization of joint stops, the dynamics of an open-chained multijoint manipulator (Equation (4.2)) is modified to be

${... ... \cdot \cdot . . ... n_{M_{i} i . (Θ . Θ) . {\overset{..}{Θ}}_{i} . +} ... n = 1 n_{M_{i} 1 . \cdot (Θ . . Θ .) . \cdot {\overset{..}{Θ}}_{i} . \cdot +} . . nn . n . . \cdot Γ_{n i^{k}}^{\cdot} {\dot{Θ}}_{i} {\dot{Θ}}_{k} . + \cdot N_{n} (Θ, \dot{Θ}) i^{k} ... \cdot \cdot . \cdot \cdot . \cdot . . \cdot \cdot$ ${... ... \cdot \cdot . . ... n_{M_{i} i . (Θ . Θ) . {\overset{..}{Θ}}_{i} . +} ... n = 1 n_{M_{i} 1 . \cdot (Θ . . Θ .) . \cdot {\overset{..}{Θ}}_{i} . \cdot +} . . nn . n . . \cdot Γ_{n i^{k}}^{\cdot} {\dot{Θ}}_{i} {\dot{Θ}}_{k} . + \cdot N_{n} (Θ, \dot{Θ}) i^{k} ... \cdot \cdot . \cdot \cdot . \cdot . . \cdot \cdot$ (4.9)

Equations (4.3) and (4.4) are then modified to be Equations (4.10) and (4.11), respectively.

$τ_{i} + τ_{ip} - τ_{i + 1} - τ_{(i + 1) p} + τ_{id} = (J_{i} + m_{i} l_{gi}^{2} + l_{i}^{2} \sum_{j = i + 1}^{n} m_{j}) {\overset{..}{Φ}}_{i} + (m_{i} l_{gi} + l_{i} \sum_{j = i + 1}^{n} m_{j}) gcos Φ_{i} (i = 1, 2, ...' n - 1)$ $τ_{i} + τ_{ip} - τ_{i + 1} - τ_{(i + 1) p} + τ_{id} = (J_{i} + m_{i} l_{gi}^{2} + l_{i}^{2} \sum_{j = i + 1}^{n} m_{j}) {\overset{..}{Φ}}_{i} + (m_{i} l_{gi} + l_{i} \sum_{j = i + 1}^{n} m_{j}) gcos Φ_{i} (i = 1, 2, ...' n - 1)$ (4.10)

$τ_{n} + τ_{np} + τ_{nd} = (J_{n} + m_{n} l_{gn}^{2}) {\overset{..}{Φ}}_{n} + m_{n} g l_{gn} cos Φ_{n}$ $τ_{n} + τ_{np} + τ_{nd} = (J_{n} + m_{n} l_{gn}^{2}) {\overset{..}{Φ}}_{n} + m_{n} g l_{gn} cos Φ_{n}$ (4.11)

where,

$τ_{ip} = {\begin{matrix} τ_{i \dot{r} np} (Θ_{i})_{'} Θ_{i 1 b} \leq Θ_{i} \leq Θ_{im \dot{m}} \\ 0_{'} Θ_{im \dot{m}} < Θ_{i} < Θ_{ima \times} \\ τ_{ima \times p} (Θ_{i})_{'} Θ_{ima \times} \leq Θ_{i} \leq Θ_{iub} \end{matrix}$ $τ_{ip} = {\begin{matrix} τ_{i \dot{r} np} (Θ_{i})_{'} Θ_{i 1 b} \leq Θ_{i} \leq Θ_{im \dot{m}} \\ 0_{'} Θ_{im \dot{m}} < Θ_{i} < Θ_{ima \times} \\ τ_{ima \times p} (Θ_{i})_{'} Θ_{ima \times} \leq Θ_{i} \leq Θ_{iub} \end{matrix}$

is the passive torque generated by the joint stop mounted on joint i.(θ_imin, θ_imax) is the free rotation range of joint i. [9_flb, 9,_min] and [0,_max, 9_iub] are the action ranges of joint stops in clockwise and counterclockwise directions, respectively.

According to Equations (4.10) and (4.11), it is possible to utilize the passive torque resulting from the joint stop as part of the driving torque in the joint, similar to the utilization of dynamically coupled driving to improve the capability of hyper dynamic manipulation for the whole manipulator Actually, this is also due to the transference of power from the base to the end-effector through the contact of joint stops Additionally, the load capability of the end-effector can be improved to exceed the limitation of the active torque of actuators when the link is in contact with the joint stop

Another useful method is forming the joint stop by the mechanism configuration of a manipulator itself. That is, by contacting one arm with another arm, this contact can be regarded as an available joint stop In this case, some flexible skin on the arm is necessary to supply elastic and damping characteristics This is especially useful for the redundant manipulator Because the utilization of this kind of joint stop is similar to the aforementioned joint stop, the following discussions are limited to the case of the structural joint stop.

4.2.3 Case Study: Mechanism Design of a Golf Swing Robot

As a case study to utilize dynamically coupled driving and joint stops in a manipulator, a golf swing robot with a smart structure is considered that can imitate the golf swing motion by a human

Figure 4.4 shows an overview of the developed prototype of the golf swing robot and its configuration. The robot consists of a base frame, the first joint (shoulder joint), an arm, the second joint (wrist joint), and a club. The first joint is to realize the equivalent function of shoulder in human and is driven by a direct drive (DD) motor, which is suitable for dynamically coupled driving In the second joint a small DD motor with two joint stops to realize the function of wrist in human is used The small DD motor in the wrist joint is selected so that its load capability is only a little greater than the static torque due to the weight of the club Because a small DD motor is used in the wrist joint, the structure of the wrist joint, as well as that of the whole manipulator, becomes very compact and light; that is, smart Distribution of the actuators is an important point to realize hyper dynamic manipulations in a smart structure On the other hand, the small DD motor in the wrist joint does not directly contribute to the acceleration of the wrist joint in a high-speed swing motion Therefore, in this mechanism, the dynamic manipulation is mainly realized by the power of the DD motor in the shoulder joint; that is, dynamically coupled driving is to be utilized for hyper dynamic manipulations

The detailed structure of the joint stops is shown in Figure 4.5. Each joint stop consists of a pair of magnets and a shock absorber The elastic force is derived from the repelling force between two magnets, and the viscous force is generated by the absorber. The approximate equation of the elastic characteristic of the joint stops is shown in Equation (4.12).

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FIGURE 4.4

Prototype of golf swing robot.

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FIGURE 4.5

Detailed structure of the joint stop.

$T_{2 s} to p_{-} char (Θ_{2 s}) = a_{0} + a_{1} Θ_{2 s} + a_{2} Θ_{2 s}^{2} + a_{3} Θ_{2 s}^{2} + a_{4} Θ_{2 s}^{4} + a_{5} Θ_{2 s}^{5} + a_{6} Θ_{2 s}^{6} (412)$ $T_{2 s} to p_{-} char (Θ_{2 s}) = a_{0} + a_{1} Θ_{2 s} + a_{2} Θ_{2 s}^{2} + a_{3} Θ_{2 s}^{2} + a_{4} Θ_{2 s}^{4} + a_{5} Θ_{2 s}^{5} + a_{6} Θ_{2 s}^{6} (412)$

$a_{0} = 1.164 \times 10,$ $a_{0} = 1.164 \times 10,$ $a_{1} = - 2.915 \times 10,$ $a_{1} = - 2.915 \times 10,$ $a_{2} = 3.724 \times 1 0^{- 1},$ $a_{2} = 3.724 \times 1 0^{- 1},$ $a_{3} = - 2.675 \times 1 0^{- 2}$ $a_{3} = - 2.675 \times 1 0^{- 2}$

$a_{4} = 1.060 \times 1 0^{- 3},$ $a_{4} = 1.060 \times 1 0^{- 3},$ $a_{5} = - 2.141 \times 1 0^{- 5},$ $a_{5} = - 2.141 \times 1 0^{- 5},$ $a_{6} = 1.715 \times 1 0^{- 7}$ $a_{6} = 1.715 \times 1 0^{- 7}$ (4.12)

The action range of the joint stops is from 8_2s = 0 [deg ] to 8_2s = 20 [deg]. The role of the shock absorber is to absorb the collision between the arm and the club, and the shock absorber used here can absorb a velocity difference up to 9. 3 rad/s.

Therefore, the passive torque in the wrist joint generated by the joint stops can be represented by the following equation:

$τ_{2 p} = {_{τ_{2 p}}^{τ_{2 min_{max} p'}} 0,, Θ_{2 m \dot{m}} < Θ_{2} < Θ_{2 max} Θ_{21 b} \leq Θ_{2} \leq Θ_{2 min} Θ_{2 max} \leq Θ_{2} \leq Θ_{2 ub}$ $τ_{2 p} = {_{τ_{2 p}}^{τ_{2 min_{max} p'}} 0,, Θ_{2 m \dot{m}} < Θ_{2} < Θ_{2 max} Θ_{21 b} \leq Θ_{2} \leq Θ_{2 min} Θ_{2 max} \leq Θ_{2} \leq Θ_{2 ub}$ (4.13)

where

$τ_{2 minp} = τ_{2 sto p_{-} char} (2 0^{\circ} - | Θ_{2 min} - Θ_{2} |)$ $τ_{2 minp} = τ_{2 sto p_{-} char} (2 0^{\circ} - | Θ_{2 min} - Θ_{2} |)$ $τ_{2 maxp} = - τ_{2 sto p_{-} char} (2 0^{\circ} - | Θ_{2} - Θ_{2 max} |)$ $τ_{2 maxp} = - τ_{2 sto p_{-} char} (2 0^{\circ} - | Θ_{2} - Θ_{2 max} |)$

When the club rotates in the clockwise direction, the passive torque will be generated after the club enters the action range of the joint stop from 8_2min to 8_2lb. Likewise, when the club rotates in the counterclockwise direction, the passive torque will be generated after the club enters the action range of the joint stop from 6_2max to 8_2ub.

4.3 Method to Utilize Dynamically Coupled Driving and Joint Stops

Some methods for controlling a manipulator with a passive joint using dynamically coupled driving have been proposed (Arai and Tachi 1991; De Luca and Oriolo 2002; Nakamura, Koinuma, and Suzuki 1996). The proposed methods are interesting and effective for the manipulator with a complete passive joint. For the hyper dynamic manipulator proposed in this chapter, these methods cannot be applied directly. Herein, we use a control method based on motion generation.

According to the foregoing statements, to improve the capability of dynamic manipulation, dynamically coupled driving must be made use of efficiently by adopting light and low-power actuators in a manipulator and one special motion trajectory, and the joint stop must be made available in the manipulator and utilized correctly in the motion Obviously, the utilization of both dynamically coupled driving and the joint stop depends on the motion planning. Unfortunately, to the best of our knowl-edge, there is no mature analytical method to generate such motion for a nonlinear system We solve this problem by adopting a constrained optimization method.

4.3.1 Motion Generation and Control Method

4.3.1.1 Motion Generation

Many related works have been reported regarding the motion generation of a manipulator (Wang, Timoszyk, and Bobrow 2001). Most of these optimal motion generation methods were based on joint trajectory approximation with a performance index and some constraints. In addition, general motion generation methods mainly generate the joint trajectory according to the specifications for velocity, acceleration, etc., of different joints in their joint space separately (Shimon 1999)

However, as mentioned previously, the features of this proposal are utilizing dynamically coupled driving and joint stops in a hyper dynamic manipulator to realize a smart structure like a human Therefore, it is necessary to generate hyper dynamic manipulation of a manipulator while considering the constraints on maximum active torque and the power of the actuators, the characteristics of joint stops, etc, in addition to the boundary conditions such as motion specifications. If a motion trajectory satisfies both constraints and boundary conditions, dynamically coupled driving and joint stops will be utilized automatically However, because the nonlinearity and coupling are strengthened by those constraints, the problem of motion planning becomes more difficult. Among the constraints, the hard constraint on active torque is the most pivotal factor for motion generation It was found that joint trajectory-based methods are difficult to use to solve such kinds of motion generation problems

To deal with such motion generation problems, time-dependent active torque functions of joint i(i = 1, • -, n) during the whole period from initial position to finish position are used as inputs. If the active torque functions of joint i(i = 1, ^•, n) are known, the motions of these joints can be derived by solving direct dynamics by satisfying the hard constraints on active torque and actuator power and the characteristics of joint stops We assign active torque functions of joint i(i = 1, • -, n) as the sum of a series of basis functions multiplied by coefficients and transform the optimal motion planning problem into a problem of obtaining coefficients of the basis functions, the time (t_m) when the manipulator has the specified motion specifications and finish time (tf). Therefore, the hyper dynamic manipulation that utilizes dynamically coupled driving and joint stops efficiently becomes the solution of such a constrained optimization problem

$τ_{i} (t) = \sum_{j = 1}^{p} c_{ij} B_{j} (t), (i = 1 n)$ $τ_{i} (t) = \sum_{j = 1}^{p} c_{ij} B_{j} (t), (i = 1 n)$ (4.14)

where 0 < t < tf, B_;(t) is the basis function, and c_{j is the coefficient of basis function.

The coefficients of the basis function and the time durations to satisfy the boundary conditions

$(Θ (0), \dot{Θ} (0), \overset{..}{Θ} (0), Θ (t_{m}), \dot{Θ} (t_{m}), \overset{..}{Θ} (t_{m}), Θ (t_{f}), \dot{Θ} (t_{f}), \overset{..}{Θ} (t_{f})$ $(Θ (0), \dot{Θ} (0), \overset{..}{Θ} (0), Θ (t_{m}), \dot{Θ} (t_{m}), \overset{..}{Θ} (t_{m}), Θ (t_{f}), \dot{Θ} (t_{f}), \overset{..}{Θ} (t_{f})$

with different cost functions (J) can be derived by numerical iterative calculation shown in Equation (4.15) (w_l, w₂, and w₃ are weighting factors). Then the solution of torque inputs for optimal motion and optimal motion itself can be generated simultaneously by calculation. Motion generation is performed by considering the hard constraints on the load capability of actuators and the constraints of two-direction joint stops.

$minC (τ, t_{m}, t_{f})$ $minC (τ, t_{m}, t_{f})$ (4.15)

subject to dynamics Equation (4.9), the initial conditions

$Θ (0) = Θ_{0}, \dot{Θ} (0) = 0, \overset{..}{Θ} (0) = 0$ $Θ (0) = Θ_{0}, \dot{Θ} (0) = 0, \overset{..}{Θ} (0) = 0$

and the hard constraints on the active torque |t¡| < x¡max, (i = I,---,n), where

$C (/ τ, t_{m}, t_{f}) = e (/ τ, t_{m})^{T} w_{1} e (/ τ, t_{m}) + e (/ τ, t_{f})^{T} w_{2} e (/ τ, t_{f}) + w_{3} J (/ τ)$ $C (/ τ, t_{m}, t_{f}) = e (/ τ, t_{m})^{T} w_{1} e (/ τ, t_{m}) + e (/ τ, t_{f})^{T} w_{2} e (/ τ, t_{f}) + w_{3} J (/ τ)$

$e (τ, t_{m}) = e (Θ (t_{m}), \dot{Θ} (t_{m}), \overset{..}{Θ} (t_{m}),$ $e (τ, t_{m}) = e (Θ (t_{m}), \dot{Θ} (t_{m}), \overset{..}{Θ} (t_{m}),$ $Θ_{m}, {\dot{Θ}}_{m}, {\overset{..}{Θ}}_{m})$ $Θ_{m}, {\dot{Θ}}_{m}, {\overset{..}{Θ}}_{m})$

is the error function of the motion specifications at time t_m .

$e (τ, t_{f}) = e (Θ (t_{f}), \dot{Θ} (t_{f}), \overset{..}{Θ} (t_{f}),$ $e (τ, t_{f}) = e (Θ (t_{f}), \dot{Θ} (t_{f}), \overset{..}{Θ} (t_{f}),$ $Θ_{f}, {\dot{Θ}}_{f}, {\overset{..}{Θ}}_{f})$ $Θ_{f}, {\dot{Θ}}_{f}, {\overset{..}{Θ}}_{f})$

is the finish conditions of the motion.

$Θ = [Θ_{1'} Θ_{n}]^{T}$ $Θ = [Θ_{1'} Θ_{n}]^{T}$

4.3.1.2 Control Method

Generally, a computed torque method with linear feedback compensation can be adopted to realize trajectory tracking, based on the linearization and decoupling of a nonlinear and coupled system. However, for a hyper dynamic manipulator, because of the assumption of utilizing dynamically coupled driving and the ultra-high-motion speed, the real-time problem of control becomes more difficult compared to that of conventional manipulators even when adopting a computed torque method with linear feedback compensation. Therefore, a simplified feedforward system with a proportional-derivative (PD) controller is adopted instead of computed torque method.

4.3.2 Case Study: Motion Generation and Control of a Golf Swing Robot

As a study case, herein we discuss the motion generation and control of the real golf swing robot shown in Figure 4.4. For simplicity, we assume that the motion of the golf swing robot is on a plane, called a swing plane, and consider the motion of the arm and the club only According to the above assumption, a simple model of the golf swing robot is used as shown in Figure 4.6.

The motion equation of the model can be represented by Equation (4.16), where the driving torque of the wrist joint is the sum of the active torque by the actuator and the passive torque by the joint stops shown in Equation (4.17). As the characteristics of the joint stop, a mathematical model of the passive torque shown by Equation (4.18) is considered. The hard constraints on the active torque are represented in Equation (4.19).

$τ_{1} = M_{11} {\overset{..}{Θ}}_{1} + M_{12} {\overset{..}{Θ}}_{2} + h_{122} {\dot{Θ}}_{2}^{2} + 2 h_{112} {\dot{Θ}}_{1} {\dot{Θ}}_{2} + g_{1} τ_{2} + τ_{2 p} = M_{21} {\overset{..}{Θ}}_{1} + M_{22} {\overset{..}{Θ}}_{2} + h_{211} {\dot{Θ}}_{1}^{2} + g_{2}$ $τ_{1} = M_{11} {\overset{..}{Θ}}_{1} + M_{12} {\overset{..}{Θ}}_{2} + h_{122} {\dot{Θ}}_{2}^{2} + 2 h_{112} {\dot{Θ}}_{1} {\dot{Θ}}_{2} + g_{1} τ_{2} + τ_{2 p} = M_{21} {\overset{..}{Θ}}_{1} + M_{22} {\overset{..}{Θ}}_{2} + h_{211} {\dot{Θ}}_{1}^{2} + g_{2}$ (4.16)

where

$τ_{2 p} = {\begin{matrix} τ_{2 m \dot{m} p'} 24 0^{o} = Θ_{21 b} \leq Θ_{2} \leq Θ_{2 m \dot{m}} = 26 0^{o} \\ 0, 26 0^{o} = Θ_{2 min} < Θ_{2} < Θ_{2 max} = 46 0^{o} \\ τ_{2 maxp'} 46 0^{o} = Θ_{2 max} \leq Θ_{2} \leq Θ_{2 ub} = 48 0^{o} \end{matrix}$ $τ_{2 p} = {\begin{matrix} τ_{2 m \dot{m} p'} 24 0^{o} = Θ_{21 b} \leq Θ_{2} \leq Θ_{2 m \dot{m}} = 26 0^{o} \\ 0, 26 0^{o} = Θ_{2 min} < Θ_{2} < Θ_{2 max} = 46 0^{o} \\ τ_{2 maxp'} 46 0^{o} = Θ_{2 max} \leq Θ_{2} \leq Θ_{2 ub} = 48 0^{o} \end{matrix}$ (4.17)

images

FIGURE 4.6

Model of a two-joint golf swing robot.

$τ_{2 minp} = τ_{2 sto p_{-} char} (2 0^{\circ} - | Θ_{2 min} - Θ_{2} |) τ_{2 maxp} = - τ_{2 sto p_{-} char} (2 0^{\circ} - | Θ_{2 max} - Θ_{2} |)$ $τ_{2 minp} = τ_{2 sto p_{-} char} (2 0^{\circ} - | Θ_{2 min} - Θ_{2} |) τ_{2 maxp} = - τ_{2 sto p_{-} char} (2 0^{\circ} - | Θ_{2 max} - Θ_{2} |)$ (4.18)

$|' τ_{1} | \leq' τ_{1 max} |' τ_{2} | \leq' τ_{2 ma \times}$ $|' τ_{1} | \leq' τ_{1 max} |' τ_{2} | \leq' τ_{2 ma \times}$ (4.19)

(θ_2min θ_2max) is the free rotation range of joint 2.

The main specifications of the DD motor (DR1130E00(H), Yokogawa Precision Co., Japan) used in the shoulder joint and the DD motor (D100-30, Nikki Denso Co., Japan) used in the wrist joint are shown in Table 4.1. The boundary conditions for motion specifications are shown in Table 4.2.

Here, we assign the active torque functions of joint 1 and joint 2 as a Fourier time series

TABLE 4.1

Main Specifications of DD Motors

	Shoulder Joint	Wrist Joint
Max. torque (Nm)	110	9.8
Max. speed (rps)	4.3	5
Max. power (W)	3,000	70
Resolution of resolver (PPR)	31,9488	338,840
Weight (kg)	32	1.6

TABLE 4.2

Boundary Conditions

	t = t₀ = 0 (Address Time)	t = t_m (Impact Time)	t = t_f (Finish Time)
θ(deg)	θ₁₀ = 270 θ₂₀ = 0	θ_im = 270 θ_2m = 0	N/A
θ (rad/s)	θ₁₀ = 0 θ₂₀ = 0	v_ym = (m/s)	θ_1f = 0 θ_2f = 0
θ (rad/s2)	θ₁₀ = 0 θ₂₀ = 0	N/A	θ_1f = 0 θ_2f = 0

t = t₀ = 0

(Address Time)

t = t_m

(Impact Time)

t = t_f

(Finish Time)

θ(deg)

θ₁₀ = 270

θ₂₀ = 0

θ_im = 270

θ_2m = 0

N/A

θ (rad/s)

θ₁₀ = 0

θ₂₀ = 0

v_ym = (m/s)

θ_1f = 0

θ_2f = 0

θ (rad/s2)

θ₁₀ = 0

θ₂₀ = 0

N/A

θ_1f = 0

θ_2f = 0

${\begin{matrix} τ_{1} (t) = a_{0} + \sum_{n = 1}^{p} a_{2 nhyphen 1} cos (nt / k t_{f} + a_{2 n}) \\ τ_{2} (t) = b_{0} + \sum_{n = 1}^{q} b_{2 nhyphen 1} cos (nt / k t_{f} + b_{2 n}) \end{matrix}$ ${\begin{matrix} τ_{1} (t) = a_{0} + \sum_{n = 1}^{p} a_{2 nhyphen 1} cos (nt / k t_{f} + a_{2 n}) \\ τ_{2} (t) = b_{0} + \sum_{n = 1}^{q} b_{2 nhyphen 1} cos (nt / k t_{f} + b_{2 n}) \end{matrix}$ (4.20)

where 0 < t < t_f, k > 0.

Considering the motion specifications shown in Table 4.2, the detailed motion generation model is expressed by Equation (4.21). Herein, t_m is the time to realize the desired motion specifications, tf is the finish time, v_x is the translational speed of the club head in the X₀ direction, v_y is the transla-tional speed in the Y₀ direction, v_xm and v_ym are the desired impact speeds in the X₀ and Y₀ directions, and 9_m is the desired impact position. 6 f = 0 and 6f = 0 are the stop conditions of the manipulator without considering the stop position

$minC (τ, t_{m}, t_{f})$ $minC (τ, t_{m}, t_{f})$ (4.21)

subject to Equations (4.16), (4.17), (4.18), (4.19) and the initial conditions

where

$C (τ, t_{m}, t_{f}) = e (τ, t_{m})^{T} w_{1} e (τ, t_{m}) + e (τ, t_{f})^{T} w_{2} e (τ, t_{f}) + w_{3} J (τ) e (τ, t_{m}) = [Θ (t_{m}) - Θ_{m},$ $C (τ, t_{m}, t_{f}) = e (τ, t_{m})^{T} w_{1} e (τ, t_{m}) + e (τ, t_{f})^{T} w_{2} e (τ, t_{f}) + w_{3} J (τ) e (τ, t_{m}) = [Θ (t_{m}) - Θ_{m},$ $v_{χ} (t_{m}) - v_{xm},$ $v_{χ} (t_{m}) - v_{xm},$ $v_{y} (t_{m}) - v_{ym}] e (τ, t_{f}) = [\dot{Θ} (t_{f}) - {\dot{Θ}}_{f'} . \overset{..}{Θ} (t_{f}) - {\overset{..}{Θ}}_{f}] Θ = [Θ_{1'} Θ_{2}]^{T}$ $v_{y} (t_{m}) - v_{ym}] e (τ, t_{f}) = [\dot{Θ} (t_{f}) - {\dot{Θ}}_{f'} . \overset{..}{Θ} (t_{f}) - {\overset{..}{Θ}}_{f}] Θ = [Θ_{1'} Θ_{2}]^{T}$

The other parameters for simulation are determined according to the average values of human beings and are omitted here.

The following cost function toward minimizing the total work consumed by the actuators of joint 1 and joint 2 is used.

$J = \int_{0}^{t_{f}} | τ_{1} (t) \cdot {\dot{Θ}}_{1} (t) | dt + \int_{0}^{t_{f}} | τ_{2} (t) \cdot {\dot{Θ}}_{2} (t) | dt$ $J = \int_{0}^{t_{f}} | τ_{1} (t) \cdot {\dot{Θ}}_{1} (t) | dt + \int_{0}^{t_{f}} | τ_{2} (t) \cdot {\dot{Θ}}_{2} (t) | dt$ (4.22)

DD motors are set to torque mode and are controlled by torque (voltage) reference from the computer. Angular positions of joints are measured through resolvers and counters by a board computer

As characteristics of DD motors, coulomb friction torque and viscous friction torque must be compensated for because they cannot be neglected in the case of DD motors. Coulomb friction torque is calculated according to the relation between the reference voltage input to the motor driver and the output torque produced by the motor and is calibrated by experiments. Viscous friction coefficients are also calculated according to the experimental results of the relation between the voltage reference and the angular velocity

As an implementation of the control system to the real manipulator, we constructed a controller shown in Figure 4.7. Considering the features of the robot, such as high speed, strong nonlinearity, and dynamic coupling, a feed-forward compensation is introduced with a PD controller. That is, the torque feed-forward compensations of joints combined with PD controllers for the angular positions of joints are used The torques of joints for feed-forward compensation and the reference motions of joints for PD controller are generated by offline calculation according to the method described previously, before the swing starts. Sampling time for a feed-forward and feedback loop is 1 ms.

images

FIGURE 4.7

Control system.

4.4 Simulation and Experimental Results for the Golf Swing Robot

4.4.1 Simulation

Using the above-discussed motion generation method, simulations of the golf swing motion with joint stops for an impact speed of 25 m/s are imple-mented and the results are shown in Figure 4.8. From Figure 4.8, the following features can be concluded.

1. In the backswing phase from the address position to the top position, the arm and the club are taken back by their motors just like in conventional motion control, because the angular velocity in this period is not so high.

2. During the downswing phase, the shoulder joint is accelerated first, and the wrist joint is accelerated later At the beginning of the downswing, the wrist joint is kept in contact with the joint stop and a large constraint (passive) torque by the joint stop is generated (Figures 4.8b and 4.8d) This passive torque plays an important role in the initial acceleration of the wrist joint, because the active torque by the wrist joint is too small to accelerate the wrist joint itself at the beginning of the downswing. Just before the impact time, the shoulder joint is decelerated first, but the wrist joint is still accelerated rapidly to realize a very high head speed at the impact time (Figure 4.8b). This multistep acceleration is due to the utilization of dynamically coupled driving in joint 2, as discussed in Section 4.2. From Figure 4.8e, it can be observed that the dynamically coupled driving torque of joint 2 is mainly utilized to accelerate the golf club (Figure 4.6) in the downswing phase.

3. In the follow-through phase from impact position to finish position, an inverse behavior to that in the downswing period can be observed That is, the wrist joint is decelerated and stopped mainly by dynamically coupled driving torque and passive torque (Figures 4.8d and 4.8e). Then the shoulder joint is decelerated and stopped by its motor.

images

FIGURE 4.8

Simulation results with joint stops for V_xm = 25 m/s: (a) angle, (b) angular velocity. (continued) Simulation results with joint stops for V_xm = 25 m/s: (c) torque; (d) passive torque of joint 2. Simulation results with joint stops for V_xm = 25 m/s: (e) dynamically coupled driving torque of joint 2

4.4.2 Experiments

By using the developed prototype shown in Figure 4.4 and the control system shown in Figure 4.7, experiments in various conditions have been done to validate the simulation results. As an example, a comparison between the swing without the joint stops (the joint stops are removed from the robot) and the swing with the joint stops is shown.

The experimental results of angle, angular velocity, and torques of each joint during the swing are shown in Figures 4.9 and 4.10. The case of not using the joint stops is presented in Figure 4.9, and Figure 4.10 presents the results obtained when using the joint stops It is important to note that these experimental results are consistent with those obtained through the simulation (Figure 4.8).

By comparing Figures 4.9 and 4.10 the following can be concluded:

1. A compact swing can be realized by using joint stops (Figure 4.10a). That is, the angular displacement from the address position to the top position of the shoulder joint becomes smaller.

images

FIGURE 4.9

Experimental result without joint stop for V_xm = 25 m/s: (a) angle, (b) angular velocity. Experimental result without joint stop for V_xm = 25 m/s: (c) torque, (d) dynamically coupled driving torque of joint 2.

images

FIGURE 4.10

Experimental result with joint stop for V_xm = 25 m/s: (a) angle, (b) angular velocity. Experimental result with joint stop for V_xm = 25 m/s: (c) torque, (d) passive torque. Experimental result with joint stop for V_xm = 25 m/s: (e) dynamically coupled driving torque of joint 2.

2. The maximum torque of the shoulder joint becomes much smaller due to the joint stop (Figure 4.10c).

Therefore, it is concluded that an efficient hyper dynamic manipulation is achieved by way of using dynamically coupled driving and joint stops in the smart structure manipulator

4.5 Conclusion

To improve the capability of a manipulator, especially the capability for hyper dynamic manipulation, a basic concept of utilizing dynamically coupled driving and structural joint stops in a manipulator inspired by humans has been proposed To show the feasibility of this proposal, a prototype of a hyper dynamic manipulator, namely, a golf swing robot, has been developed Experimental results show that hyper dynamic manipulation can be realized efficiently by the smart structure manipulator, through using such disposition of actuators and joint stops in the manipulator. It can be expected that this approach will serve as a general way toward realizing hyper dynamic manipulations for robots; for example, humanoid robots.

References

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De Luca, A. and Oriolo, G. 2002. Trajectory planning and control for planar robots with passive last joint. The International Journal of Robotics Research, 21(5-6): 575-590.

Hayakawa, Y., Kawamura, S., Goto, T., and Nagai, K. 1996. Development of a revolving drive mechanism for a robot manipulator by using pneumatic bellows actuators with force sensing ability. Journal of the Robotics Society of Japan, 14(2): 271-278. (in Japanese)

Hirzinger, G., Albu-Schaffer, A., Hahnle, M., Schaefer, I., and Spofer, N.. 2001. On a new generation of torque controlled light-weight robots. Paper read at the IEEE International Conference on Robotics and Automation, Seoul, Korea, May 21-26

Hogan, N. 1985. An approach to manipulation. ASME Journal of Dynamics, Systems, Measurement and Control, 107: 1-24.

Kagami, S., Nishiwaki, K., Sugihara, T., Kuffner, J J, Jr, Inaba, M., and Inoue, H 2001 Design and implementation of software research platform for humanoid Robotics: H6 Paper read at the IEEE International Conference on Robotics and Automation, Seoul, Korea, May 21-26

Katsurashima, W., Kikuchi, H., Abe, K., and Uchiyama, M. 1998. Design and development of a robot arm with flexible joints. Paper read at the RSJ Annual Conference, Hakkaido, Japan, September 18-20. (in Japanese)

Laurin-Kovitz, K. F., Colgate, J. E., and Carnes, S. D. R. 1991. Design of components for programmable passive impedance Paper read at the IEEE International Conference on Robotics and Automation, Sacremento, CA, April 9-11

Ming, A., Harada, N., Shimojo, M., and Kajitani, M 2003 Development of a hyper dynamic manipulator utilizing joint stops Paper read at the International Conference on Intelligent Robots and Systems, Las Vegas, NV, October 27-31.

Ming, A., Kajitani, M., and Shimojo, M 2002 A proposal for utilizing structural joint stop in a manipulator Paper read at the International Conference on Robotics and Automation

Ming, A., Mita, T., Dhlamini S, and Kajitani, M 2001 Motion control skill in human hyper dynamic manipulations—An investigation on the golf swing by simulation Paper read at the IEEE International Symposium on Computational Intelligence in Robotics and Automation, Alberta, Canada, July 29-August 1

Mizuuchi, I., Matsuki, T., Kagami, S., Inaba, M., and Inoue, H. 1998. An approach to a humanoid that has a variable flexible torso. Paper read at the RSJ Annual Conference, Hakkaido, Japan, September 18-20.. (in Japanese)

Morita, T., Tomita, N., Ueda, T., and Sugano, S. 1998. Development of force-controlled robot arm using mechanical impedance adjuster Journal of the Robotics Society of Japan, 16(7): 1001-1006. (in Japanese)

Murray, R.M., Li, Z., and Sastry, S. S. 1994. A Mathematical Introduction to Robotic Manipulation . Boca Raton, FL: CRC Press.

Nagasaka, K., Kuroki, Y., Suzuki, S., Itoh, Y., and Yamaguchi, J 2004 Integrated motion control for walking, jumping and running on a small bipedal entertrain-ment robot Paper read at the IEEE International Conference on Robotics and Automation, New Orleans, LA, April 26-May 1

Nakamura, Y., Koinuma, M., and Suzuki, T 1996 Chotic behavior and nonlinear control of a two-joint planar arm with a free joint-control of noholonomic mechanisms with drift Journal of the Robotics Society of Japan, 14(4): 602-611

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Table of Contents for
4 Human.Inspired Hyper Dynamic Manipulation

4

Human-Inspired Hyper Dynamic Manipulation

CONTENTS

4.1 Introduction

4.2 Basic Concept

4.2.1 Utilization of Dynamically Coupled Driving

4.2.2 Utilization of Structural Joint Stop

4.2.3 Case Study: Mechanism Design of a Golf Swing Robot

4.3 Method to Utilize Dynamically Coupled Driving and Joint Stops

4.3.1 Motion Generation and Control Method

4.3.1.1 Motion Generation

4.3.1.2 Control Method

4.3.2 Case Study: Motion Generation and Control of a Golf Swing Robot

4.4 Simulation and Experimental Results for the Golf Swing Robot

4.4.1 Simulation

4.4.2 Experiments

4.5 Conclusion

References

Table of Contents for 4 Human.Inspired Hyper Dynamic Manipulation

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Human-Inspired Hyper Dynamic Manipulation

CONTENTS

Table of Contents for
4 Human.Inspired Hyper Dynamic Manipulation