The paper presents a design of an 8-DOF biped robot and its gait generation as it walks down on an inclined surface. Authors used the ZMP method for the gait generation. In the abstract, you noted: "A dynamic model of the biped is developed using Lagrange-Euler dynamics to determine the joint torques during walk on inclined ground." These is a common method to compute the dynamic walking model of the biped robot. This sentence should be dropped. In the abstract, you have talk about the genetic algorithm., but in the introduction section, you have not.

You used the ZMP method for gait generation and to ensure the balance of the biped robot during walking. Although the ZMP method has been widely used in the literature, but it is known that with such method, there is a huge consumption of energy. In you work, you have analyzed the energy consumed during walk for four different designs of the compliant shanks and then you have got the best one having the least energy consumption. But, the energy consumption of this best designed shank is still high!!!

The ZMP-based walking method was known as the static walking method. Using such method, the biped robot is very slow. Some improvements on this method have been achieved (a discussion should be given here). However, the velocity of still low. Moreover, to improve this, some authors used the dynamic walking method. A discussion and possible use of this method should be given.

Furthermore, in the dynamic walking, there are several analyses of bipedal walking using different shapes of the feet and knees. It was shown that the energy consumption depends also the shape of the two legs. In addition, to improve the energy consumption, it is possible to consider passive joints and hence you will have an underactuated biped robot. This is possibility. Another method is to control the biped robot by following some passive or semi-passive dynamic walking of the biped robot. A discussion should be given in this paper to improve the quality of presentation, discussion and comparison with other related works.

What you mean by Slope = 5/10, is Slope = 0.5 degree?

There some grammatical errors. Authors should correct and improve the entire paper.

Some suggestions for the references: - Mathematical simulation of a seven link biped robot on various surfaces and ZMP considerations - Mathematical simulation of combined trajectory paths of a seven link biped robot

One way to make sure you remember is to always include line numbers in your changes. That way, you actually have to make the change first before including the line numbers in your response.

Comments - The authors could strengthen and significantly improved the paper by answering the given comments

Statement - Discussion to produce a more contextualized statement

Statement 1:

To ensure the dynamic stability of a walking robot, several authors focused on walking pattern synthesis based on zero moment point control, prior to energy minimization.

Statement 2:

Optimal trajectory generation is an essential part of robotics. Various kinds of walking pattern generation for biped walking robots based on energy consumption have been applied. Stability of the biped walking robot is strongly affected by horizontal hip motion. Therefore, to have a stable walking special care should be taken in defining the horizontal motion of the hip.

Statement 3:

Avoidance of impact reduces the control difficulty and enhances the system stability. This achieved by keeping the velocity of the swing heel-touch zero before the impact. Regarding to repeatability and continuity conditions.

Statement 4:

The amount of global rotation of the robot during the stance phase can be described by the angular momentum with respect to the ankle point F, which can be calculated with the general formula.

Statement 5:

Stationary balancing and steady-state locomotion both require control of foot placement at touchdown to obtain or maintain stability. Lagrangian dynamics methods are based on the exchange of energy between kinetic and potential forms, with the external forces and torques represented by the virtual work terms.

Comment 1:

Author given the torque network, but sequence position data and Angular position data, ground reaction forces not plotted.

Statement 6:

The ZMP has to be located between the two ankle points in order to avoid tipping over. The physical length of the feet outside the area between the ankle points is neglected, such that the stability region indeed corresponds to the line connecting the two ankle points.

Both the vertical reaction forces in the two ankle points have to remain positive. Recall that exploiting foot rotation requires an accurate tracking of the ZMP and imposes high demands on the control system.

The ZMP trajectory is a smooth curve as the case of walk on flat horizontal terrain. ZMP trajectory is inside the convex hull of the feet support during a waking step but it is a little back side the stance foot.

Comment 2:

Author need to provide Motion on a non-horizontal ground. For example The ZMP has to lie between 0 and λ cos α, with α being the angle of the sloped surface with respect to the horizontal reference axis.

Statement 7:

Theoretically, if this natural trajectory would be used as a reference trajectory, then the corresponding ankle torque would be zero at all times.

Comment 3:

The discrete variation of the generalized velocities due to the inelastic impulsive impact with the ground can be calculated.

When the control algorithm generates the reference trajectories, Is it possible to take all these constraints into account and calculate the most ideal trajectories depending on the criterion that is used ?

Comment 4:

Author need to provide a solution. Ex: L1 and L2 are two constraints which express the fact that the robot does not slip and does not bounce back respectively. Note that XE and YE represent the coordinates of the landing position of the foot (Author can take actual parameters).

Statement 8:

To reduce the complexity in the computation and implementation, constraints are placed on the forward kinematic to decouple the leg motion such that a unique solution for the inverse kinematics is achievable. The amount of foot clearance must be sufficient to ensure that the toe and heel do not strike against the ground.

Comment 5:

As per representation Table 4: Input Parameters for spline trajectory generation in inclined terrain expressed properly.

Due to the fact that (Author should provide a problem statement, derived part of the statement for this example)

Ex (Consider Original Parameter): OFG of the upper body G coincides with the hip joint, the angular velocity of the upper body remains unchanged during the shock. Indeed since the percussion on the upper body acts on the hip joint, it can not generate a torque around G.

Statement 9:

Angular compensation does not correct the displacement errors in the walk direction for the frontal and sagittal plane movements. The model of the impact compresses the impact event into an instantaneous moment in time, resulting in a discontinuity in the velocities.

Simulation results of the compliant-link bipeds for different pelvis link heights and step lengths are presented. Author proposed a new design of a complaint joint biped robot for walking up a slope.

Response 1: A discussion on walking pattern generation and ZMP is included in the Introduction.

Response 2: The equations for the hip motion trajectory are included in the subsection Kinematics, Equation 13. The swing leg trajectory and side tilt angle trajectory are included in Equation 5.

Response 3: The repeatability and continuity conditions are taken as a constraint equation.

Response 4: The unbalanced angular momentum is calculated and the ground reaction force at the feet.

Comment 1: Yes, The position data is plotted for both rigid and compliant biped and the angular position data is plotted. Stationary reference point that is located by a position vector. When a biped-walking machine has a steady walking gait, the ZMP and lower-limbs movement can be considered periodical. Author need to provide or denote the resulting ground reaction force and moment. So, it is very important to understand the relationship between the moving coordinate system and the inertial frame, where hypothetically, they are parallel.

Comment 2: Yes of course, while calculating the ZMP there would be small errors in terms of link masses etc. that would displace the ZMP from the straight line. Differences between hip and center of mass were observed for intracyclic velocity variations (respectively, for a p<0.001), and the negative mean error value found (−0.06) evidenced a tendency of the hip to overestimate the center of mass velocity variation. It is possible to conclude that the hips forward movements might provide a good estimate.

Response 5: Authors have used ZMP equation in vector form, which also includes the slope of the ground surface. The equation for ZMP is updated. All the ZMP plots on slope shown in this paper have been derived based on this equation and the ZMP trajectories plotted on the sloped surfaces. The normal on the inclined surface is given by 'n' that indicated the inclination angle.

Response 6: The ZMP tends to move away from the straight line connecting the ankles. Also while calculating the ZMP there would be small errors in terms of link masses etc. that would displace the ZMP from the straight line.

Comment 3: However, when using the hip as a measure of forward velocity and/or displacement, the associated error should always be taken into consideration.

Response 7: Small variation on the velocity happens due to small errors in deflection calculations and dynamics model. Active control would be able to correct these errors in real time, but this is not in the scope of this paper.

Statement 1: Yes, This was mainly because the biped robot was not controlled in close loop to follow the input simulation trajectory. The point on the ground where the total moments of the active forces equal zero. If the ZMP is within the convex hull of all contact points between the feet and the ground, dynamically stable walking motion can be achieved.

Statement 2: A jerky movement of the pelvis trajectory is visible around the middle of the step. Knee and ankle joint trajectories are relatively smooth. In Experimental results, It is necessary to create a table for Important experiment parameters. All the pitch rotation motors of both legs are attached in the opposite direction from one another. More stable walking is achieved using balanced foot contact controls.