### Table 1: Common quadruped gaits and relative phases of legs (1).

"... In PAGE 2: ...A detailed study of biped and quadruped gaits may be found in the paper by Alexander (1) including a list of some commonly found gaits in animals, see Table1 . The list is not exhaustive, and the relative phases given for the respective gaits are not fixed but may vary depending on the shape and size of the animal.... In PAGE 2: ... Reptiles, for example, trot even during slow walking (1). Not given in Table1 are the duty factors which describe the fraction of time that a leg is in... In PAGE 7: ... Figure 3 displays the optimal relative phases for both the amble and trot gaits at their optimal velocity. The amble relative phases differ from Table1 , most likely due to the particular construction of our quadruped, see Table 2. Figure 3 also illustrates how the optimal hybrid trajectories of each gait pattern correspond to the hybrid automaton presented in Figure 1.... ..."

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### Table 2. Measured SSM for hexapod and quadruped A similar response for the three PCRG algorithms can be appreciated. The addition of the control loop increased noticeably the robot stability margin. Also, for higher support factors the SSM increased as should be expected in the geometric model. It must be noticed that replacing the FFNN in the previous model, by the parametric description of the leg trajectory, the synthesized walking patterns do not exhibit any undesired vibration. For simulated and real conditions, the quadruped robot was able to walk over a terrain with a low slope in a case, and with uneven weight distribution for the other. In both cases the measured SSM was improved by using BFP reference generator.

"... In PAGE 15: ...2 Experimental Results Using the model previously described it is possible to synthesize several gait modes for both simulated and real quadrupeds, and for a simulated hexapod. The performance of the model for the SSM values using different PCRG as control references can be evaluated in Table2... ..."

### Table 2: Column 1 lists the primary and secondary gaits produced by quad. Column 2 lists the associated rhythms of the hindlegs of these gaits, as they appear in leg. Column 3 lists the leg/arm rhythms in arm of solutions corresponding to a small symmetry-breaking perturbation of a quadruped gait type solution.

in Abstract

2006

"... In PAGE 13: ... However, if a periodic solution in quad is perturbed to a periodic solution in arm, then the signals sent to an ipsilateral arm and leg will be approximately shifted by a quarter-period, which, as noted, does not agree with the interlimb coordination patterns of a biped walk. Moreover, as summarized in the second column of Table2 , the only quad gait that could correspond to a biped walk is the quadruped walk.... In PAGE 14: ... At the simplest level, we observe that with one exception each known biped gait, as modeled in leg can be obtained by focusing on the hindleg rhythms in standard gaits found in quad. See Table2 . The exception is the asymmetric hop, which is curious because the only observation of this gait that we can nd is in birds [45].... ..."

### TABLE I PHASE LAGS NECESSARY TO PRODUCE WALKING GAITS IF A CHAIN OF FOUR OSCILLATORS IS CONNECTED TO THE MOTORS THAT DRIVE THE LEGS OF A ROBOT AS DESCRIBED IN THE TEXT.

2006

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### Table 3: Gait motions for controlling walking speed

2005

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### Table 1. (a) The table shows the phase di erences corresponding to the three most common gaits observed in quadrupeds. (b) The table shows the 3 di erent rotation angles that are needed in the construction of the ACPO-CPG. (c) Connection scheme used for the ACPO-CPG.

2004

"... In PAGE 9: ...ay: left front 1, left hind 2, right hind 3, right front 4 (cf. Fig. 1(c)). If we de ne d;ij = i j as the di erence between the phase of limb i and j then, the gaits can be classi ed according to Table1 (a) (the phases are normalized: = 1 corresponds to the full circle). A quadruped CPG is constructed from four fully connected ACPO, i.... In PAGE 9: ... First of all, for this gait pattern the phase di erence between the pairs of oscillators that are connected need to be known. We can derive these phase di erences by help of Table1 (a). Then, for each connection a corresponding rotation matrix can be derived.... In PAGE 9: ... By analysis of the requirements needed to generate walk, trot and bound we come up with three parameter sets of R (cf. Table1 (b)). Instead Table 1.... In PAGE 9: ...hen a parameter Pgait is increased. We chose the functions given in 33-35. This allows to chose the gait pattern by the single continuous valued parameter Pgait. The three corresponding rotation matrices are used in the connection scheme as presented in Table1... ..."

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### Table 1 summarizes the types of basic gaits of the Planar Walker. Because the gaits are initial-state dependent, they are categorized into two major groups according to the states of the cylinders: fully retracted or fully extended. Gaits with identical initial states can be used alternatively right away because the final state of the prior gait is identical to the initial state of the subsequent gait. A transition sequence is needed between gaits with different initial states. This transition sequence can be obtained using a finite automaton called a gait generator [12].

"... In PAGE 2: ... Table1 : Notations and pose changes of gaits x y N E S W N E S W {A} {B} p1 p2 p3 p4 pab pG pS Figure 5: Pose change of the robot 3. KINEMATICS OF BASIC GAITS In this section, we study the kinematics of the robot based on the execution of a series of gaits.... ..."

### Table 1. Gait parameters

1999

"... In PAGE 2: ... The horizontal velocity of the body is controlled only during the double support phase. The gait and virtual component parameters which affect the walking pattern and performance of the planar biped are summarized in Table1 and Table 2 respectively. The virtual forces for both the single and the double support phases are transformed into the joint space using the equations derived in [4,5].... ..."

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### Table 2: Physical data of the quadruped model. Link Mass Length Radius

"... In PAGE 7: ... Figure 3 displays the optimal relative phases for both the amble and trot gaits at their optimal velocity. The amble relative phases differ from Table 1, most likely due to the particular construction of our quadruped, see Table2 . Figure 3 also illustrates how the optimal hybrid trajectories of each gait pattern correspond to the hybrid automaton presented in Figure 1.... ..."

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### Table 3: Symmetry groups of standard gaits of the eight-cell CPGs. Symmetry pairs (H; K) of standard quadrupeds gaits (quad) and symmetry pairs (H0; K0) of bipeds gaits (arm). The identi cation of bipedal gaits can be found in Section 2.1.

in Abstract

2006

"... In PAGE 11: ... An analogous argument is valid for H0. In Table3 we list the spatiotemporal symmetry types of primary and secondary quadru- pedal gaits in quad computed in [24]. Given a periodic solution corresponding to one of these gait types, we break symmetry by a small perturbation in the associated system of di erential equations and observe that the perturbed periodic solution has the symmetry groups in arm described above.... In PAGE 12: ...Table3 . Note that all of the spatiotemporal symmetry groups of leg rhythms in bipeds can be obtained as symmetry groups of perturbed symmetric solutions of quad.... ..."