**3. Locomotion stabilization**

### **3.1. Internal model**

In order to realize a robust robotic locomotion in any environment, two abilities are required: planning of the suitable motion based on the recognition of moving environment, and evaluation of generated motion. Then we propose the internal model based on a prediction and feedback as shown in Fig. 4.

Prediction for locomotion plans the locomotion form based on environmental information. Environmental information is sensed by a laser range finder; then the robot determines the suitable gait for the environment. In this research, biped and quadruped walking is focused as the gaits. The robot selects biped walking in the environment that is easy to walk such as flat

#### 4 Will-be-set-by-IN-TECH 24 Injury and Skeletal Biomechanics Locomotion Transition Scheme of Multi-Locomotion Robot <sup>5</sup>

terrain. Meanwhile the robot selects quadruped walking in the environment that is difficult to walk in biped state such as slope or rough terrain. Also, the robot plans the walking steps and landing position of the selected gait based on recognized terrain. Previously, we designed this prediction for locomotion [20].

among phenomenon using probability. We describe the causality between the risk of falling

In this research, Bayesian Network shown in Fig. 5 is used to estimate the risk of falling down. First, Bayesian Network estimates Robot Model Reliability "*R*" and Environmental Model Reliability "*E*". Reliability of a Robot Model *R* show how ideal the robot motion is,

S

R E

X2 X3

ZMP trajectory error Touchdown timing Accuracy of ground recognition

Risk of falling down (Stability of walking)

> Environmental model reliability (Reliability of external dynamics)

Locomotion Transition Scheme of Multi-Locomotion Robot 25

0

0. 5

1

1. 5

2

2

E R

down and the uncertain parameters.

Robot model reliability (Reliability of Internal states)

X1

**Figure 5.** Bayesian Network for locomotion stabilization

0

**Figure 6.** Probability for Biped Walking

0

0. 2

0. 4

0. 6

0. 8

1 P(S|R,E)

0. 5

1

1. 5

Stability margin

The feedback for locomotion evaluates walking stability based on internal condition of the robot. In this chapter, we propose the method of estimating the risk of falling down using Bayesian Networks (BN). In estimating the risk, we set "Robot Model Reliability (Reliability of Internal states)" and "Environmental Model Reliability (Reliability of External dynamics)". Reliability of a robot model shows how far difference between reality motion and locomotion algorithm is, or physical abilities of robot. For example, if the robot has motor trouble, this is low and the risk of falling down is high. Reliability of an environmental model shows how accurately a robot recognizes environment. If robots move in dark, it does not get information of environment, so this parameter is low and the risk of falling down is high. In biped and quadruped walking, the robot evaluates both reliabilities, estimate the risk of falling down and attain an optimum gait adapting to the environments or the conditions. This feedback for locomotion is explained in the next section.

### **3.2. Stabilization based on internal conditions**

### *3.2.1. Estimation of falling down risk*

In this chapter, we consider the uncertainty caused by motion and recognition as the factor of realization of locomotion. Approximation of motion algorithm is pointed out as uncertainty caused by motion. Most robots have models to simplify calculating dynamics. Thus, this gives robot systems uncertainty because there are difference between a reality robot shape and a robot model. Uncertainty caused by recognition is accuracy of sensors, effective ranges of sensor or abstraction of environment. There are many kinds of uncertain parameters which have various dimensions, so it is difficult to deal with them uniformly. Then, these parameters are integrated into the risk of falling down as belief with Bayesian Network. The Bayes theory assumes that parameters have distributions individually, and posterior probability is induced formally by conditional probability. Bayesian Network is the model which describes relations

**Figure 4.** Locomotion stabilization scheme

among phenomenon using probability. We describe the causality between the risk of falling down and the uncertain parameters.

In this research, Bayesian Network shown in Fig. 5 is used to estimate the risk of falling down. First, Bayesian Network estimates Robot Model Reliability "*R*" and Environmental Model Reliability "*E*". Reliability of a Robot Model *R* show how ideal the robot motion is,

**Figure 5.** Bayesian Network for locomotion stabilization

4 Will-be-set-by-IN-TECH

terrain. Meanwhile the robot selects quadruped walking in the environment that is difficult to walk in biped state such as slope or rough terrain. Also, the robot plans the walking steps and landing position of the selected gait based on recognized terrain. Previously, we designed this

The feedback for locomotion evaluates walking stability based on internal condition of the robot. In this chapter, we propose the method of estimating the risk of falling down using Bayesian Networks (BN). In estimating the risk, we set "Robot Model Reliability (Reliability of Internal states)" and "Environmental Model Reliability (Reliability of External dynamics)". Reliability of a robot model shows how far difference between reality motion and locomotion algorithm is, or physical abilities of robot. For example, if the robot has motor trouble, this is low and the risk of falling down is high. Reliability of an environmental model shows how accurately a robot recognizes environment. If robots move in dark, it does not get information of environment, so this parameter is low and the risk of falling down is high. In biped and quadruped walking, the robot evaluates both reliabilities, estimate the risk of falling down and attain an optimum gait adapting to the environments or the conditions. This feedback for

In this chapter, we consider the uncertainty caused by motion and recognition as the factor of realization of locomotion. Approximation of motion algorithm is pointed out as uncertainty caused by motion. Most robots have models to simplify calculating dynamics. Thus, this gives robot systems uncertainty because there are difference between a reality robot shape and a robot model. Uncertainty caused by recognition is accuracy of sensors, effective ranges of sensor or abstraction of environment. There are many kinds of uncertain parameters which have various dimensions, so it is difficult to deal with them uniformly. Then, these parameters are integrated into the risk of falling down as belief with Bayesian Network. The Bayes theory assumes that parameters have distributions individually, and posterior probability is induced formally by conditional probability. Bayesian Network is the model which describes relations

Planing for locomotion

Locomotion 1 Locomotion 2 Locomotion 3 Locomotion 4

Modification Modification Modification Modification

Transiton

Evalution of stability

prediction for locomotion [20].

locomotion is explained in the next section.

*3.2.1. Estimation of falling down risk*

Internal Conditon

**Figure 4.** Locomotion stabilization scheme

Environmental Infomation

**3.2. Stabilization based on internal conditions**

**Figure 6.** Probability for Biped Walking

*3.2.2. COG trajectory error X*<sup>1</sup>

the probability variable *X*1.

*3.2.3. Touchdown timing X*<sup>2</sup>

*3.2.4. Accuracy of ground recognition X*<sup>3</sup>

approximate algorithm have the uncertainty.

**3.3. Consideration of stability margin**

*3.3.1. Consideration of stability margin*

follows:

The position of the center of gravity is measured by the force sensor which the robot put on its four legs. In biped posture, outputs which come from the sixth axis force sensor makes ZMP. In quadruped posture, the center of gravity is calculated with the equilibrium of moments. Then the errors between the desired trajectory and the observed trajectory decides

Locomotion Transition Scheme of Multi-Locomotion Robot 27

The touchdown timing shows differences between the landing and the ground surface actually. When the robot is thrown off balance, or when the recognition is inadequate and the ground is higher than measured point, then the touchdown timing is earlier than the planed

This parameter evaluates the performance of the recognition which the robot has. This shows how much information the robot attain with some sensors, and how abstracted the environmental model which the robot has is. The laser range finder has effective ranges, so over this ranges there is much uncertainty. Then the two-dimension recognition and the

The conditional probability *P*(*S* | *R*, *E*) describes the influence which Reliability of a Robot Model *R* have with the Risk of falling down *S*. Then when the stability margin is enough large compared with the COG errors, the influence is little even if *R* goes down. In reverse, when the stability margin is small, *R* has a big influence on *S*. Therefore *P*(*S* | *R*, *E*) is decided based on the stability margin. For example, a stability margin in biped posture is smaller than one in quadruped posture, so *P*(*S* | *R*, *E*) in biped posture is larger than in quadruped posture.

The conditional probability *P*(*S* | *R*, *E*) describes the influence which Reliability of a Robot Model *R* have with the Risk of falling down *S*. Then when the stability margin is enough large compared with the COG errors, the influence is little even if *R* goes down. In reverse, when the stability margin is small, *R* has a big influence on *S*. Therefore *P*(*S* | *R*, *E*) is decided based on the stability margin. Thus, *P*(*S* | *R*, *E*) is changed by designing the revised value of conditional probability Δ*P*(*S* | *R*, *E*) shown in Fig. 8 according to the stability margine as

*kmax*

<sup>Δ</sup>*P*(*<sup>S</sup>* <sup>|</sup> *<sup>R</sup>*, *<sup>E</sup>*) = <sup>−</sup> <sup>2</sup>Δ*<sup>P</sup>*

*P*(*S* | *R*, *E*) = *P*(*S* | *R*, *E*) + Δ*P*(*S* | *R*, *E*), (2)

*k* + Δ*P*, (3)

0 ≤ *k* ≤ *kmax*, (4)

timing. In the robot moving, the probability variable *X*<sup>2</sup> is renewed at every landing.

**Figure 7.** Probability for Quadruped Walking

and describes the capacity of moving. Reliability of an Environmental Model *E* is an index which shows how correctly the robot perceive the dynamics between the environment and the robot. Secondly, *R* and *E* are induced the risk of falling down "*S*". "*S* = 1" shows falling down, and "*S* = 0" shows not falling down. Probability variables *R* and *E* have classes 0, 1, 2 in more reliable order. Then conditional probability *P*(*S* | *R*, *E*) reflects the performance of the robot, and the designer arranges this probability subjectively. Probability distribution of biped walking is different from quadruped walking so that *P*(*S* | *R*, *E*) of biped walking is higher than quadrupled one. Fig.6 and Fig.7show *P*(*S* | *R*, *E*) of biped walking and quadruped walking respectively. The evaluating parameters *X*1, *X*2, *X*<sup>3</sup> shown below are observed at real time. Then probability variables from 0 to 4 based on uncertainty which the parameters have input the Bayesian Network. When the probability variable is 0, the situation is most stable. The calculation of Bayesian Network uses the enumeration method shown by (1).

$$\begin{aligned} P(S=1) &= \frac{\sum\_{R=0}^{2} \sum\_{E=0}^{2} P(S=1, R, E)}{\sum\_{1}^{1} \sum\_{2}^{2} \sum\_{E=0}^{2} P(S, R, E)}\\ &= \sum\_{R=0}^{2} \sum\_{E=0}^{2} P(S=1 \mid R, E) P(R \mid X\_{1}, X\_{2}) P(E \mid X\_{2}, X\_{3}) \\ &= \frac{\sum\_{1}^{2} \sum\_{2}^{2}}{\sum\_{1} \sum\_{E=0}^{2} \sum\_{E=0}^{2} P(S \mid R, E) P(R \mid X\_{1}, X\_{2}) P(E \mid X\_{2}, X\_{3})} \end{aligned} \tag{1}$$

The evaluating parameters *X*1, *X*2, *X*<sup>3</sup> are always observed, so each probability *P*(*X*1), *P*(*X*2), *P*(*X*3) is set 1.

### *3.2.2. COG trajectory error X*<sup>1</sup>

6 Will-be-set-by-IN-TECH

0

(1)

0. 5

1

1. 5

2

2

and describes the capacity of moving. Reliability of an Environmental Model *E* is an index which shows how correctly the robot perceive the dynamics between the environment and the robot. Secondly, *R* and *E* are induced the risk of falling down "*S*". "*S* = 1" shows falling down, and "*S* = 0" shows not falling down. Probability variables *R* and *E* have classes 0, 1, 2 in more reliable order. Then conditional probability *P*(*S* | *R*, *E*) reflects the performance of the robot, and the designer arranges this probability subjectively. Probability distribution of biped walking is different from quadruped walking so that *P*(*S* | *R*, *E*) of biped walking is higher than quadrupled one. Fig.6 and Fig.7show *P*(*S* | *R*, *E*) of biped walking and quadruped walking respectively. The evaluating parameters *X*1, *X*2, *X*<sup>3</sup> shown below are observed at real time. Then probability variables from 0 to 4 based on uncertainty which the parameters have input the Bayesian Network. When the probability variable is 0, the situation is most stable.

R E

0

**Figure 7.** Probability for Quadruped Walking

*P*(*S* = 1) =

2 ∑ *R*=0

1 ∑ *S*=0

2 ∑ *E*=0

2 ∑ *R*=0

2 ∑ *E*=0

=

*P*(*X*1), *P*(*X*2), *P*(*X*3) is set 1.

0

0. 2

0. 4

0. 6

0. 8

1 P(S|R,E)

0. 5

1

1. 5

The calculation of Bayesian Network uses the enumeration method shown by (1).

2 ∑ *E*=0

*P*(*S* = 1, *R*, *E*)

*P*(*S*, *R*, *E*)

The evaluating parameters *X*1, *X*2, *X*<sup>3</sup> are always observed, so each probability

*P*(*S* = 1 | *R*, *E*)*P*(*R* | *X*1, *X*2)*P*(*E* | *X*2, *X*3)

*P*(*S* | *R*, *E*)*P*(*R* | *X*1, *X*2)*P*(*E* | *X*2, *X*3)

2 ∑ *R*=0

1 ∑ *S*=0

2 ∑ *E*=0

2 ∑ *R*=0 The position of the center of gravity is measured by the force sensor which the robot put on its four legs. In biped posture, outputs which come from the sixth axis force sensor makes ZMP. In quadruped posture, the center of gravity is calculated with the equilibrium of moments. Then the errors between the desired trajectory and the observed trajectory decides the probability variable *X*1.

### *3.2.3. Touchdown timing X*<sup>2</sup>

The touchdown timing shows differences between the landing and the ground surface actually. When the robot is thrown off balance, or when the recognition is inadequate and the ground is higher than measured point, then the touchdown timing is earlier than the planed timing. In the robot moving, the probability variable *X*<sup>2</sup> is renewed at every landing.

### *3.2.4. Accuracy of ground recognition X*<sup>3</sup>

This parameter evaluates the performance of the recognition which the robot has. This shows how much information the robot attain with some sensors, and how abstracted the environmental model which the robot has is. The laser range finder has effective ranges, so over this ranges there is much uncertainty. Then the two-dimension recognition and the approximate algorithm have the uncertainty.

### **3.3. Consideration of stability margin**

The conditional probability *P*(*S* | *R*, *E*) describes the influence which Reliability of a Robot Model *R* have with the Risk of falling down *S*. Then when the stability margin is enough large compared with the COG errors, the influence is little even if *R* goes down. In reverse, when the stability margin is small, *R* has a big influence on *S*. Therefore *P*(*S* | *R*, *E*) is decided based on the stability margin. For example, a stability margin in biped posture is smaller than one in quadruped posture, so *P*(*S* | *R*, *E*) in biped posture is larger than in quadruped posture.

#### *3.3.1. Consideration of stability margin*

The conditional probability *P*(*S* | *R*, *E*) describes the influence which Reliability of a Robot Model *R* have with the Risk of falling down *S*. Then when the stability margin is enough large compared with the COG errors, the influence is little even if *R* goes down. In reverse, when the stability margin is small, *R* has a big influence on *S*. Therefore *P*(*S* | *R*, *E*) is decided based on the stability margin. Thus, *P*(*S* | *R*, *E*) is changed by designing the revised value of conditional probability Δ*P*(*S* | *R*, *E*) shown in Fig. 8 according to the stability margine as follows:

$$P(S \mid \mathbb{R}, E) = P(S \mid \mathbb{R}, E) + \Delta P(S \mid \mathbb{R}, E),\tag{2}$$

$$
\Delta P(S \mid R, E) = -\frac{2\Delta P}{k\_{\text{max}}}k + \Delta P\_{\prime} \tag{3}
$$

$$0 \le k \le k\_{\text{max}} \tag{4}$$

**Figure 8.** Revised Probability Value According to Stability Margin.

where Δ*P* is the maximum revised value of conditional probability and *kmax* is the maximum stability margin.

0 <sup>D</sup> 1

*4.2.1. Experiment 1: gait selection based on falling down risk (biped to quadruped)*

than *β* (0.7). And snapshots of the experiment is shown in Fig. 14.

*4.2.2. Experiment 2: gait selection based on falling down (quadruped to biped)*

and the risk is less than *α*(0.3). Fig. 16 shows the snapshots of the experiment 2.

(=0.3) (=0.7) <sup>J</sup>

In this experiment, the robot walks on rough ground. There are inequalities which have the maximum height, 5[mm]. This is not recognized by the robot on purpose. We confirmed whether the robot in biped posture changes the gait to quadruped mode because the risk

Fig. 10 shows results about the COG trajectories come from the force sensors. And the COG trajectories induce *X*<sup>1</sup> shown in Fig. 11. Fig. 12 describes the probability variable *X*2. The numbers in these figures are the threshold to apportion the probability variable. In this experiment the node *X*1, *X*<sup>2</sup> have 0, 1, 2, 3, 4 as the probability variables. When the probability variable is 4, the robot almost falls down. The node *X*<sup>3</sup> is always 0 because the robot move within the effective ranges of the laser range finder in this experiment. Thus, Fig. 13 is the risk estimated by Bayesian Network. In the transition motion, the risk is 0.0. We can see the transition caused by the risk increasing. Before the robot conducts a squat, the risk is more

The experiment 2 confirms the transition of locomotion form when the robot starts walking in quadruped state and is given shaking disturbances made by human. Fig. 15 shows the estimated risk of falling down derived from the same way in the experiment 1. The risk of falling down is set 0 during transition from quadruped to biped walking. The risk of falling down is temporarily increased due to the shaking disturbances from human. It is confirmed that the robot stop and selects biped walking as locomotion form after disturbances stopped

QuadrupedWalking

a3

BipedWalking a1 a2

E

Risk of Falling down :Rf

Locomotion Transition Scheme of Multi-Locomotion Robot 29

Stop

**Figure 9.** Velocity - Risk of falling down

**4.2. Experimental results**

increases.

V4

V1

V3 V2

Velocity :v

### *3.3.2. Switching of locomotion mode*

The evaluating parameters *X*1, *X*2, *X*<sup>3</sup> are observed at real time, and the probability of falling down is estimated. The conditional probabilities used in Bayesian Network are arranged by the subjective judgments of the designer. Therefore, when the robot falls down, the probability of falling down is not always 1.0. So we pay an attention to the fluctuation of the probability. That is, when the robot move in biped posture and the risk of falling down increases, then it has the transition motion from biped to quadruped posture and go quadruped walking. Contrarily the risk decreases in quadruped walking, the robot stands up and go biped walking.

### **4. Experiments**

### **4.1. Experimental conditions**

In this experiment, the robot measures the landform with the laser range finder at starting point, and in walking, it get the gait based on the risk of falling down estimated by Bayesian Network shown in Fig. 9. When the risk is more than *β* (0.7) in biped posture, the robot squats to get quadruped posture. And when the risk is less than *α* (0.3) in quadruped posture, it standups. Then the robot in biped posture has three patterns of biped walking *a*1, *a*2, *a*<sup>3</sup> which have different efficiency. If the risk decreases, the robot get more efficient gait. In this research, this efficiency is the walking velocity, then *a*1, *a*2, *a*<sup>3</sup> are respectively 8.67, 6.67, 4.67[cm/sec] acquired by stride widths changed and the quadruped walking velocity is 3.00[cm/sec]. Both the standup motion and the squat motion take 10[sec] to action. Modifications of its gait are conducted in every walking cycle. The robot aims at minimizing the risk and maximizeing the efficiency all the time.

**Figure 9.** Velocity - Risk of falling down

### **4.2. Experimental results**

8 Will-be-set-by-IN-TECH

'*P(S|R,E)*

'*P*

'*P*

stability margin.

and go biped walking.

**4.1. Experimental conditions**

the efficiency all the time.

**4. Experiments**

*3.3.2. Switching of locomotion mode*

**Figure 8.** Revised Probability Value According to Stability Margin.

0 *k*

where Δ*P* is the maximum revised value of conditional probability and *kmax* is the maximum

The evaluating parameters *X*1, *X*2, *X*<sup>3</sup> are observed at real time, and the probability of falling down is estimated. The conditional probabilities used in Bayesian Network are arranged by the subjective judgments of the designer. Therefore, when the robot falls down, the probability of falling down is not always 1.0. So we pay an attention to the fluctuation of the probability. That is, when the robot move in biped posture and the risk of falling down increases, then it has the transition motion from biped to quadruped posture and go quadruped walking. Contrarily the risk decreases in quadruped walking, the robot stands up

In this experiment, the robot measures the landform with the laser range finder at starting point, and in walking, it get the gait based on the risk of falling down estimated by Bayesian Network shown in Fig. 9. When the risk is more than *β* (0.7) in biped posture, the robot squats to get quadruped posture. And when the risk is less than *α* (0.3) in quadruped posture, it standups. Then the robot in biped posture has three patterns of biped walking *a*1, *a*2, *a*<sup>3</sup> which have different efficiency. If the risk decreases, the robot get more efficient gait. In this research, this efficiency is the walking velocity, then *a*1, *a*2, *a*<sup>3</sup> are respectively 8.67, 6.67, 4.67[cm/sec] acquired by stride widths changed and the quadruped walking velocity is 3.00[cm/sec]. Both the standup motion and the squat motion take 10[sec] to action. Modifications of its gait are conducted in every walking cycle. The robot aims at minimizing the risk and maximizeing

*kmax*

### *4.2.1. Experiment 1: gait selection based on falling down risk (biped to quadruped)*

In this experiment, the robot walks on rough ground. There are inequalities which have the maximum height, 5[mm]. This is not recognized by the robot on purpose. We confirmed whether the robot in biped posture changes the gait to quadruped mode because the risk increases.

Fig. 10 shows results about the COG trajectories come from the force sensors. And the COG trajectories induce *X*<sup>1</sup> shown in Fig. 11. Fig. 12 describes the probability variable *X*2. The numbers in these figures are the threshold to apportion the probability variable. In this experiment the node *X*1, *X*<sup>2</sup> have 0, 1, 2, 3, 4 as the probability variables. When the probability variable is 4, the robot almost falls down. The node *X*<sup>3</sup> is always 0 because the robot move within the effective ranges of the laser range finder in this experiment. Thus, Fig. 13 is the risk estimated by Bayesian Network. In the transition motion, the risk is 0.0. We can see the transition caused by the risk increasing. Before the robot conducts a squat, the risk is more than *β* (0.7). And snapshots of the experiment is shown in Fig. 14.

### *4.2.2. Experiment 2: gait selection based on falling down (quadruped to biped)*

The experiment 2 confirms the transition of locomotion form when the robot starts walking in quadruped state and is given shaking disturbances made by human. Fig. 15 shows the estimated risk of falling down derived from the same way in the experiment 1. The risk of falling down is set 0 during transition from quadruped to biped walking. The risk of falling down is temporarily increased due to the shaking disturbances from human. It is confirmed that the robot stop and selects biped walking as locomotion form after disturbances stopped and the risk is less than *α*(0.3). Fig. 16 shows the snapshots of the experiment 2.

<sup>0</sup> <sup>5</sup> <sup>10</sup> <sup>15</sup> <sup>20</sup> <sup>25</sup> <sup>30</sup> <sup>35</sup> <sup>40</sup> <sup>0</sup>

Rough ground

0 5 10 15 20 25 30 35 40

Squat

Error 0.25 - 0.50 [sec]

Error 0.80 - [sec] Threshold for node X2

Error 0.50 - 0.80[sec]

Squat

Rough ground

Locomotion Transition Scheme of Multi-Locomotion Robot 31

Time[sec]

Time[sec]

QuadrupedWalk

0.5 1 1.5 2 2.5 3 3.5 4 4. 5 5

**Figure 12.** Experimental data of node *X*<sup>2</sup>

Risk of Falling down

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

**Figure 13.** Risk of falling down (Experiment 1)

  Error 0.00 - 0.10 [sec]

BipedWalk

Error 0.10 - 0.25 [sec]

Node X2 Data

**Figure 10.** Comparison between desired and actual ZMP trajectory

**Figure 11.** Experimental data of node *X*<sup>1</sup>

**Figure 12.** Experimental data of node *X*<sup>2</sup>

10 Will-be-set-by-IN-TECH

BipedWalk Squat

<sup>0</sup> <sup>5</sup> <sup>10</sup> <sup>15</sup> <sup>20</sup> <sup>25</sup> <sup>30</sup> <sup>35</sup> <sup>40</sup> -0.2

<sup>0</sup> <sup>5</sup> <sup>10</sup> <sup>15</sup> <sup>20</sup> <sup>25</sup> <sup>30</sup> <sup>35</sup> <sup>40</sup> <sup>0</sup>

Squat

Threshold for BipedWalk Threshold for QuadrupedWalk

Rough ground

Error 0.08 - 0.15 [m] Error 0.22 - 0.35 [m]

Time[sec]

QuadrupedWalk

Error 0.35 - [m]

Error 0.1 - 0.22 [m]

Error 0.05 - 0.1 [m]

Error 0.00 - 0.05 [m]

Time[sec]

0

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

**Figure 11.** Experimental data of node *X*<sup>1</sup>

Node X1 Data

0.2

0.4

0.6

0.8

ZMP Trajectory [m]

1

Desired Data Observed Data

**Figure 10.** Comparison between desired and actual ZMP trajectory

Error 0.15 - [m]

Error 0.00 - 0.02 [m]

Error 0.02 - 0.05 [m]

Error 0.05 - 0.08 [m]

**Figure 13.** Risk of falling down (Experiment 1)

<sup>0</sup> <sup>10</sup> <sup>20</sup> <sup>30</sup> <sup>40</sup> <sup>50</sup> <sup>60</sup> <sup>0</sup>

Quadruped BipedWalk

Stop Standup

Time[sec]

Locomotion Transition Scheme of Multi-Locomotion Robot 33

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

**Figure 15.** Risk of falling down (Experiment 2)

Walk

Disturbance

Risk of Falling down

**Figure 14.** Snapshots of the experiment 1

**Figure 15.** Risk of falling down (Experiment 2)

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0.0[sec] 5.0[sec] 10.0[sec]

15.0[sec] 20.0[sec] 25.0[sec]

30.0[sec] 35.0[sec] 40.0[sec]

45.0[sec] 50.0[sec] 55.0[sec]

**Figure 14.** Snapshots of the experiment 1

**5. Conclusion**

**Author details** Tadayoshi Aoyama

Yasuhisa Hasegawa

**6. References**

This chapter firstly designed internal model composed of gait planning and stability evaluation. Next, the falling down risk is estimated by integrating stability evaluation parameters that has uncertainty using the Bayesian Network. Then we proposed the stabilization method that selects the suitable locomotion form according to the change of the falling down risk. Finally, the suitable locomotion transition is experimentally realized. Although we dealt with only biped walk and quadruped walk in this chapter, we will try to deal with other locomotion modes such as brachation and ladder climbing for transition.

Locomotion Transition Scheme of Multi-Locomotion Robot 35

*Department of Complex Systems Engineering, Hiroshima University, Japan.* Taisuke Kobayashi, Zhiguo Lu, Kosuke Sekiyama and Toshio Fukuda *Department of Micro-Nano Systems Engineering, Nagoya University, Japan.*

*Department of Intelligent Interaction Technologies, University of Tsukuba, Japan.*

Journal of robotics Research. 22(3-4): 187-202.

Journal of Robotics Research. 26(5): 475-490.

on Robotics and Automation. Albuquesrque, pp.494-500.

Models in Hardware. Springer-Verlag, pp. 65-86.

[1] Fukuoka, Y., Kimura, H., and Cohen A. H. (2003) Adaptive Dynamic Walking of a Quadruped Robot on Irregular Terrain based on Biological Concepts. International

[2] Kimura, H., Fukuoka, Y. and Cohen, A. H. (2007) Adaptive Dynamic Walking of a Quadruped Robot on natural Ground based on Biological Concepts. The International

[3] Hirose, S. (2000) Variable Constraint Mechanism and Its Application for Design of Mobile Robots. The International Journal of Robotics Research. 19(11): 1126-1138. [4] Wooden, D., Malchano, M., Blankespoor, K., Howardy, A., Rizzi, A. and Raibert, M. (2010) Autonomous Navigation for BigDog. In: Proceedings of the 2010 IEEE International Conference on Robotics and Automation. Anchorage, pp. 4736-4741. [5] S. Hirose, K. Yoneda, and H. Tsukagoshi (1997) TAITAN VII : Quadruped Walking and Manipulating Robot on a Steep Slope. In: Proceedings of IEEE International Conference

[6] Yoshioka, T., Takubo, T., Arai, T. and Inoue, K. (2008) Hybrid Locomotion of Leg-Wheel

[7] Nishiwaki, K. and Kagami, S. (2010) Strategies for Adjusting the ZMP Reference Trajectory for Maintaining Balance in Humanoid Walking. In: Proceedings of the IEEE International Conference on Robotics and Automation. Anchorage, pp. 4230-4236. [8] Fukuda, T., Aoyama, T., Hasegawa, Y., and Sekiyama K. (2009) Multilocomotion Robot: Novel Concept, Mechanism, and Control of Bio-inspired Robot. In: Artificial Life

ASTERISK H. Journal of Robotics and Mechatronics. 20(3): pp. 403-412.

**Figure 16.** Snapshots of the experiment 2

### **5. Conclusion**

14 Will-be-set-by-IN-TECH

0.0[sec] 3.0[sec] 6.0[sec]

Niose Stop

Crawl

Crawl

Crawl + Noise

Restart

**Figure 16.** Snapshots of the experiment 2

9.0[sec] 12.0[sec] 15.0[sec]

21.0[sec] 36.0[sec] 40.0[sec]

Standup BipedWalk

44.0[sec] 48.0[sec] 52.0[sec]

This chapter firstly designed internal model composed of gait planning and stability evaluation. Next, the falling down risk is estimated by integrating stability evaluation parameters that has uncertainty using the Bayesian Network. Then we proposed the stabilization method that selects the suitable locomotion form according to the change of the falling down risk. Finally, the suitable locomotion transition is experimentally realized. Although we dealt with only biped walk and quadruped walk in this chapter, we will try to deal with other locomotion modes such as brachation and ladder climbing for transition.
