DETAILED ACTION
Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Remarks
The claims being considered in this application are those submitted on 03/07/2025. Claims 1-10 are pending.
Priority
The applicant’s claim to priority of JP2024-040334 on 03/14/2024 is acknowledged.
Information Disclosure Statement
The information disclosure statement(s) filed on 03/07/2025 has been annotated and considered.
Claim Rejections - 35 USC § 112
The following is a quotation of 35 U.S.C. 112(b):
(b) CONCLUSION.—The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention.
The following is a quotation of 35 U.S.C. 112 (pre-AIA ), second paragraph:
The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention.
Claim 5 is rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA ), second paragraph, as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor (or for applications subject to pre-AIA 35 U.S.C. 112, the applicant), regards as the invention.
The claim includes “λ =
±
ω
'
” and other variables “
θ
” and “
θ
˙
”. The variables should be defined within the claim such as they are within the specification for consistency. For example, applicant’s specification recites “From Equation (6), a set λ λof eigenvalue vectors…”. Appropriate correction is required.
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
Claims 1-10 are rejected under 35 U.S.C. 101 because the claimed invention is directed to a judicial exception of an abstract idea without significantly more.
Claim 1 recites: A posture control method of a non-linear inverted pendulum model, of which a height of a center of gravity is variable, and a trajectory of the center of gravity is an energy conserving system, using a control device, the posture control method comprising: obtaining a conservation energy function on the basis of a measured value of the center of gravity; converting the conservation energy function into a curve function; and calculating a set of eigenvectors through approximation as a convergent component and a divergent component without iterative calculation of a controllable area in a phase plot of the converted curve function and feeding back the convergent component and the divergent component that have been calculated.
Under Step 1: Claim 1 is a method.
Under Step 2A Prong 1: The claim recites an judicial exception of abstract idea of mental processes. The additional elements are crossed out.
A posture control method of a non-linear inverted pendulum model, of which a height of a center of gravity is variable, and a trajectory of the center of gravity is an energy conserving system,
A person is able to mentally, or with pen/paper, perform the steps of obtaining a conservation of energy function having received a measured value of a COG, and convert the function into a curve function, and then calculate a set of eigenvectors through approximation.
Under Step 2A Prong 2, the crossed-out items in the claim are additional elements. The "using a control device" is an additional element because it is a part of a computer being used as a tool to perform the abstract ideas. See MPEP 2106.05 (f).
Under Step 2B, the additional elements are the same as Step 2A Prong 2. For the same reasons, the additional elements also are not sufficient to amount to significantly more than the abstract idea.
**The examiner recommends adding a control step to actively recite controlling a robot to maneuver in accordance with these steps to overcome the 101 rejection, as long as there is sufficient support within the specification.
Claim 2 recites: The posture control method of claim 1, wherein the trajectory of the center of gravity is an ellipse or a hyperbola, and wherein
Under Step 2A Prong 1: The mathematical steps can be performed by a human mentally or with pen/paper.
Under Step 2A Prong 2/Step 2B: The "control device" is an additional element because it is a part of a computer being used as a tool to perform the abstract ideas. See MPEP 2106.05 (f).
Claim 3 recites: The posture control method of claim 1, wherein the curve function is a hyperbolic function, and wherein the
Under Step 2A Prong 1: The mathematical steps can be performed by a human mentally or with pen/paper.
Under Step 2A Prong 2/Step 2B: The "control device" is an additional element because it is a part of a computer being used as a tool to perform the abstract ideas. See MPEP 2106.05 (f).
Claim 4 recites: The posture control method according to claim 1, wherein the conservation energy function is set using a parametric variable.
Under Step 2A Prong 1: This is a part of the mathematical steps that can be performed by a human mentally or with pen/paper.
Claim 5 recites: The posture control method of claim 2, Wherein the linearized set λ =
±
ω
'
of eigenvectors that is the convergent component and the divergent component is obtained from the following equation:
d
d
t
θ
θ
˙
=
0
1
ω
'
2
0
θ
θ
˙
Under Step 2A Prong 1: This is a part of the mathematical steps that can be performed by a human mentally or with pen/paper.
Claim 6 recites: The posture control method according to claim 3, wherein
θ
is a state quantity of an inverted pendulum expressed in a parametric variable,
θ
˙
is a time derivative of
θ
, g
is a gravitational acceleration, C is a divergent component denominator variable, X(
θ
) is a function,
Ω
(
θ
) is a function, and x is a position in a movement direction, and wherein the asymptote is obtained using the following equation:
θ
˙
=
±
g
X
θ
C
θ
2
θ
=
±
Ω
θ
x
Under Step 2A Prong 1: This is a part of the mathematical steps that can be performed by a human mentally or with pen/paper.
Claim 7 recites: The posture control method according to claim 2, wherein Kp is a gain, Kv is a gain,
θ
is a state quantity of an inverted pendulum expressed in a parametric variable,
θ
˙
is a time derivative of
θ
τ
θ
is an input to a system, and
ω
is a slope of the divergent component and is Kp/Kv, and wherein the control device performs the feedback on the basis of the following equation:
τ
θ
=
K
p
θ
+
K
v
θ
˙
=
K
p
θ
+
1
ω
θ
˙
.
Under Step 2A Prong 1: This is a part of the mathematical steps that can be performed by a human mentally or with pen/paper.
Claim 8 recites: The posture control method according to claim 3, wherein Kp is a gain, Kv is a gain,
θ
is a state quantity of an inverted pendulum expressed in a parametric variable,
θ
˙
is a time derivative of
θ
τ
θ
is an input to a system,
ω
is a slope of the divergent component and is Kp/Kv, and
Ω
(
θ
)
is a function of
θ
, and wherein the control device performs the feedback on the basis of the following equation:
τ
θ
=
K
p
θ
+
K
v
θ
˙
=
K
p
θ
+
1
Ω
θ
θ
˙
.
Under Step 2A Prong 1: This is a part of the mathematical steps that can be performed by a human mentally or with pen/paper.
Claim 9 recites: A posture control device controlling a posture of a mobile body, the posture control device comprising: a non-linear inverted pendulum model of which a height of a center of gravity is variable, and a trajectory of the center of gravity is an energy conserving system; a function calculating unit obtaining a conservation energy function on the basis of a measured value of the center of gravity; a conversion unit converting the conservation energy function into a curve function; and a feedback unit calculating a set of eigenvectors through approximation as a convergent component and a divergent component without iterative calculation of a controllable area in a phase plot of the converted curve function and feeding back the convergent component and the divergent component that have been calculated.
Under Step 1: Claim 9 is a device.
Under Step 2A Prong 1: The claim recites an judicial exception of abstract idea of mental processes. The additional elements are crossed out.
A posture control device controlling a posture of a mobile body,
A person is able to mentally, or with pen/paper, perform the steps of obtaining a conservation of energy function having received a measured value of a COG, and convert the function into a curve function, and then calculate a set of eigenvectors through approximation.
Under Step 2A Prong 2, the crossed-out items in the claim are additional elements. The "posture control device" and various "units" are additional elements because they a part of a computer being used as a tool to perform the abstract ideas. See MPEP 2106.05 (f).
Under Step 2B, the additional elements are the same as Step 2A Prong 2. For the same reasons, the additional elements also are not sufficient to amount to significantly more than the abstract idea.
**The examiner recommends adding a control step to actively recite controlling a robot to maneuver in accordance with these steps to overcome the 101 rejection, as long as there is sufficient support within the specification.
Claim 10 recites: A computer-readable non-transient storage medium storing a program causing a computer of a control device, which controls a posture of a mobile body, having a non- linear inverted pendulum model of which a height of a center of gravity is variable, and a trajectory of the center of gravity is an energy conserving system, to: obtain a conservation energy function on the basis of a measured value of the center of gravity; convert the conservation energy function into a curve function; and calculate a set of eigenvectors through approximation as a convergent component and a divergent component without iterative calculation of a controllable area in a phase plot of the converted curve function and feedback the convergent component and the divergent component that have been calculated.
Under Step 1: Claim 10 is a non-transient computer readable medium.
Under Step 2A Prong 1: The claim recites an judicial exception of abstract idea of mental processes. The additional elements are crossed out.
A computer-readable non-transient storage medium storing a program
A person is able to mentally, or with pen/paper, perform the steps of obtaining a conservation of energy function having received a measured value of a COG, and convert the function into a curve function, and then calculate a set of eigenvectors through approximation.
Under Step 2A Prong 2, the crossed-out items in the claim are additional elements. The "computer of a control device" is an additional elements because it is a part of/a computer being used as a tool to perform the abstract ideas. See MPEP 2106.05 (f).
Under Step 2B, the additional elements are the same as Step 2A Prong 2. For the same reasons, the additional elements also are not sufficient to amount to significantly more than the abstract idea.
**The examiner recommends adding a control step to actively recite controlling a robot to maneuver in accordance with these steps to overcome the 101 rejection, as long as there is sufficient support within the specification.
Claim Rejections - 35 USC § 103
In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis (i.e., changing from AIA to pre-AIA ) for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
Claims 1, 3, and 9-10 are rejected under 35 U.S.C. 103 as being unpatentable over Pratt et. al. (2007 NPL, "Derivation and Application of a Conserved Orbital Energy for the Inverted Pendulum Bipedal Walking Model") in view of Yamamoto et. al. (2020 NPL, IDS, "Survey on Model-Based Biped Motion Control for Humanoid Robots").
Regarding Claim 1, Pratt discloses:
A posture control method of a non-linear inverted pendulum model, (See at least Page 4653 via "Given expressions for the Orbital Energy, we can compute where the foot should be placed or how the Center of Mass trajectory should be modified in order to achieve a desired velocity on the next step" and also 4658 via "…support leg was actuated to control the body’s height as a function of the horizontal distance from the foot to the body mass…" and Page 4656 via "For our system, which is nonlinear, those curves are not straight lines…" and Page 4653 via "While the Linear Inverted Pendulum model is a useful model for determining foot placement, one of its main drawbacks is that the Center of Mass trajectory is linear. In this paper, we relax the Center of Mass trajectory constraint and only constrain the trajectory to be continuous.)
of which a height of a center of gravity is variable, and a trajectory of the center of gravity is an energy conserving system, using a control device, the posture control method comprising: (See at least Page 4653 via "While the Linear Inverted Pendulum model is a useful model for determining foot placement, one of its main drawbacks is that the Center of Mass trajectory is linear. In this paper, we relax the Center of Mass trajectory constraint and only constrain the trajectory to be continuous. We derive a new expression for a conserved quantity during single support, which we refer to in this paper simply as the “Orbital Energy”" and Page 4653 via "this expression for Orbital Energy allows us to determine where to step to achieve a next step velocity, but without assuming a linear height trajectory." and Page 46653 via "…for many classes of trajectories, such as those in which height is a polynomial function of Center of Mass horizontal displacement, the Orbital Energy can be solved in closed form.")
obtaining a conservation energy function on the basis of a measured value of the center of gravity; (See at least Page 4653 via "We derive a new expression for a conserved quantity during single support, which we refer to in this paper simply as the “Orbital Energy”" and Equations (2) & (3); "where z = f(x) is the Center of Mass height as a function of the horizontal displacement from the foot to the Center of Mass…this expression for Orbital Energy allows us to determine where to step to achieve a next step velocity" and "where z = f(x) is the Center of Mass height as a function of the horizontal displacement from the foot to the Center of Mass, f′(x) is the derivative of f(x) with respect to x and g is the acceleration of gravity.")
converting the conservation energy function into a curve function; and (See at least Page 4653 via "…state space phase portraits can then be determined as they consist of curves, each corresponding to constant values of the orbital energy…" and Page 4656 via "…For different values of Orbital Energy, we get different functions of horizontal velocity versus horizontal displacement. These level curves are the phase portrait of the dynamic equations of motion.")
(See at least Page 4653 via "…to compute phase portraits for the system…In fact, for many classes of trajectories, such as those in which height is a polynomial function of Center of Mass horizontal displacement, the Orbital Energy can be solved in closed form" and Page 4656 via "These level curves are the phase portrait of the dynamic equations of motion….For a linear system, those curves would correspond to the stable and unstable eigenvectors of the system.")
However, although Pratt discloses eigenvectors corresponding to stable and unstable eigenvectors, Pratt does not explicitly disclose the specific eigenvector calculation or controllable area.
Nevertheless, Yamamoto--who is in the same field of endeavor--discloses: calculating a set of eigenvectors through approximation as a convergent component and a divergent component (See at least Page 2 via "The eigensystem analysis on the above state equation tells that it is equivalently transformed as…" and Page 13 via "…To:N-- 1 is a square matrix comprising eigenvectors of Ao:N in each column, and ηT and ξT are the time extended CCM and DCM…" **Wherein eigensystem is analyzed and transformed into convergent/divergent components)
(See at least Page 5 via Figure 2 which illustrates the "Phase portrait of COM under the ZMP constraint" and Page 4 via "The gray region in Figure 2 is a set of initial states that stably converge to the desired point (0, 0)…Consequently, the state feedback that maximizes the stable region" **Wherein the stable region is interpreted as the controllable area/region)
feeding back the convergent component and the divergent component that have been calculated (See at least Page 4 via "Consequently, the state feedback that maximizes the stable region is represented as…equation (33)…Namely, this is a feedback of the DCM" and Page 10 via "where ηG and ξG can be regarded as the CCM and the DCM, respectively, as well as η and ξ defined in Equation (16). Also, the capture region regarding β can be defined…Therefore, the control problem results in the control of β, which is also regarded as the DCM…").
Therefore, it would have been obvious to one of ordinary skill in the art prior to the effective filing date of the given invention to modify the posture control method of Pratt in view of the eigensystem and feedback used to perform control of Yamamoto as both references are directed towards posture and stability control, and as such, implementing Yamamoto's eigensystem would've yielded predictable results and provided a representation of the controls for the same type of inverted pendulum model. Furthermore, Yamamoto also discloses that the research is extending Pratt's: "Pratt and Drakunov [19] discussed the case that the spatial manifold in which the COM moves is represented as 𝔃G = f(xG), where ƒ is a twice-differentiable function with respect to xG…" [Yamamoto Page 9].
Regarding Claim 3, Modified Pratt discloses the posture control method according to Claim 1.
Furthermore, Pratt discloses: wherein the curve function is a hyperbolic function, and (See at least Figure 1 which depicts hyperbolic trajectories and Page 4656 via "These level curves are the phase portrait of the dynamic equations of motion…In Figure 1 we show such a phase portrait for the polynomial trajectory…" and "The phase trajectory which leads into the origin is defined by the points x0 and ˙x0,which correspond to an Orbital Energy of 0.0…")
…non-linear inverted pendulum model (See at least Page 4656 via "For our system, which is nonlinear, those curves are not straight lines…" and Page 4653 via "While the Linear Inverted Pendulum model is a useful model for determining foot placement, one of its main drawbacks is that the Center of Mass trajectory is linear. In this paper, we relax the Center of Mass trajectory constraint and only constrain the trajectory to be continuous.)
However, Pratt does not explicitly disclose, but Yamamoto discloses: wherein the control device feeds back an asymptote of a curve drawn by the (See at least Page 4 via "The lines £1 and £2 are parallel to the asymptotic line of the CCM and pass (Xmin, 0) and (Xmax, 0), respectively. The gray region in Figure 2 is a set of initial states that stably converge to the desired point (0, 0), which is maximized if both a and b are parallel to £1 and £2 as illustrated in Figure 3…Consequently, the state feedback that maximizes the stable region is represented…Namely, this is a feedback of the DCM")
as a convergent component and a divergent component of the (See at least Page 10 via "where ηG and ξG can be regarded as the CCM and the DCM, respectively…").
Therefore, it would have been obvious to one of ordinary skill in the art prior to the effective filing date of the given invention to modify Pratt in view of Yamamoto as both references are directed towards posture and stability control, and as such, implementing Yamamoto's feedback control would've yielded predictable results and provided a representation of the controls for the same type of inverted pendulum model. Furthermore, Yamamoto also discloses that the research is extending Pratt's: "Pratt and Drakunov [19] discussed the case that the spatial manifold in which the COM moves is represented as 𝔃G = f(xG), where ƒ is a twice-differentiable function with respect to xG…" [Yamamoto Page 9].
Regarding Claim 9, Pratt discloses:
A posture control (See at least Page 4653 via "Given expressions for the Orbital Energy, we can compute where the foot should be placed or how the Center of Mass trajectory should be modified in order to achieve a desired velocity on the next step" and also 4658 via "…support leg was actuated to control the body’s height as a function of the horizontal distance from the foot to the body mass…" and Page 4656 via "For our system, which is nonlinear, those curves are not straight lines…" and Page 4653 via "While the Linear Inverted Pendulum model is a useful model for determining foot placement, one of its main drawbacks is that the Center of Mass trajectory is linear. In this paper, we relax the Center of Mass trajectory constraint and only constrain the trajectory to be continuous.)
of which a height of a center of gravity is variable, and a trajectory of the center of gravity is an energy conserving system; (See at least Page 4653 via "While the Linear Inverted Pendulum model is a useful model for determining foot placement, one of its main drawbacks is that the Center of Mass trajectory is linear. In this paper, we relax the Center of Mass trajectory constraint and only constrain the trajectory to be continuous. We derive a new expression for a conserved quantity during single support, which we refer to in this paper simply as the “Orbital Energy”" and Page 4653 via "this expression for Orbital Energy allows us to determine where to step to achieve a next step velocity, but without assuming a linear height trajectory." and Page 46653 via "…for many classes of trajectories, such as those in which height is a polynomial function of Center of Mass horizontal displacement, the Orbital Energy can be solved in closed form.")
a (See at least Page 4653 via "We derive a new expression for a conserved quantity during single support, which we refer to in this paper simply as the “Orbital Energy”" and Equations (2) & (3); "where z = f(x) is the Center of Mass height as a function of the horizontal displacement from the foot to the Center of Mass…this expression for Orbital Energy allows us to determine where to step to achieve a next step velocity" and "where z = f(x) is the Center of Mass height as a function of the horizontal displacement from the foot to the Center of Mass, f′(x) is the derivative of f(x) with respect to x and g is the acceleration of gravity.")
(See at least Page 4653 via "…state space phase portraits can then be determined as they consist of curves, each corresponding to constant values of the orbital energy…" and Page 4656 via "…For different values of Orbital Energy, we get different functions of horizontal velocity versus horizontal displacement. These level curves are the phase portrait of the dynamic equations of motion.")
(See at least Page 4653 via "…to compute phase portraits for the system…In fact, for many classes of trajectories, such as those in which height is a polynomial function of Center of Mass horizontal displacement, the Orbital Energy can be solved in closed form" and Page 4656 via "These level curves are the phase portrait of the dynamic equations of motion….For a linear system, those curves would correspond to the stable and unstable eigenvectors of the system.")
However, although Pratt discloses eigenvectors corresponding to stable and unstable eigenvectors, Pratt does not explicitly disclose the specific eigenvector calculation or controllable area.
Nevertheless, Yamamoto--who is in the same field of endeavor--discloses: calculating a set of eigenvectors through approximation as a convergent component and a divergent component (See at least Page 2 via "The eigensystem analysis on the above state equation tells that it is equivalently transformed as…" and Page 13 via "…To:N-- 1 is a square matrix comprising eigenvectors of Ao:N in each column, and ηT and ξT are the time extended CCM and DCM…" **Wherein eigensystem is analyzed and transformed into convergent/divergent components)
(See at least Page 5 via Figure 2 which illustrates the "Phase portrait of COM under the ZMP constraint" and Page 4 via "The gray region in Figure 2 is a set of initial states that stably converge to the desired point (0, 0)…Consequently, the state feedback that maximizes the stable region" **Wherein the stable region is interpreted as the controllable area/region)
feeding back the convergent component and the divergent component that have been calculated (See at least Page 4 via "Consequently, the state feedback that maximizes the stable region is represented as…equation (33)…Namely, this is a feedback of the DCM" and Page 10 via "where ηG and ξG can be regarded as the CCM and the DCM, respectively, as well as η and ξ defined in Equation (16). Also, the capture region regarding β can be defined…Therefore, the control problem results in the control of β, which is also regarded as the DCM…").
Therefore, it would have been obvious to one of ordinary skill in the art prior to the effective filing date of the given invention to modify the posture control method of Pratt in view of the eigensystem and feedback used to perform control of Yamamoto as both references are directed towards posture and stability control, and as such, implementing Yamamoto's eigensystem would've yielded predictable results and provided a representation of the controls for the same type of inverted pendulum model. Furthermore, Yamamoto also discloses that the research is extending Pratt's: "Pratt and Drakunov [19] discussed the case that the spatial manifold in which the COM moves is represented as 𝔃G = f(xG), where ƒ is a twice-differentiable function with respect to xG…" [Yamamoto Page 9].
However, modified Pratt does not explicitly disclose the various "unit"(s).
Nevertheless, it would have been obvious to disclose a control device/specific control units because the robot necessitates a controller for the motion to be controlled, and in order for the robot to be able to move.
Regarding Claim 10, Modified Pratt discloses:
the control steps (See Claim 1 rejection as the steps are the same)
However, Modified Pratt does not explicitly disclose: A computer-readable non-transient storage medium storing a program causing a computer of a control device, which controls a posture of a mobile body
Nevertheless, it would have been obvious to one of ordinary skill in the art prior to the effective filing date of the given invention to utilize a non-transitory storage medium that stores a program because the robot necessitates instructions in order to know when/how to maneuver, and the program needs to be stored in order to be read and executed.
Claim 2 is rejected under 35 U.S.C. 103 as being unpatentable over Pratt et. al. (2007 NPL, "Derivation and Application of a Conserved Orbital Energy for the Inverted Pendulum Bipedal Walking Model") and Yamamoto et. al. (2020 NPL, IDS, "Survey on Model-Based Biped Motion Control for Humanoid Robots") in view of Morasso et. al. (2019 NPL, "Stabilization of a Cart Inverted Pendulum: Improving the Intermittent Feedback Strategy to Match the Limits of Human Performance").
Regarding Claim 2, Modified Pratt discloses the posture control method according to Claim 1.
Furthermore, Pratt discloses: wherein the trajectory of the center of gravity is an ellipse or a hyperbola, and (See at least Figure 1 which depicts hyperbolas and Page 4656 via "These level curves are the phase portrait of the dynamic equations of motion…In Figure 1 we show such a phase portrait for the polynomial trajectory…" and "The phase trajectory which leads into the origin is defined by the points x0 and ˙x0,which correspond to an Orbital Energy of 0.0…")
PNG
media_image1.png
374
354
media_image1.png
Greyscale
However, Pratt does not explicitly disclose the linearization of eigenvectors.
Nevertheless, Yamamoto discloses feeding back the eigenvectors: wherein the control device (See at least Page 4 via "Consequently, the state feedback that maximizes the stable region is represented as…equation (33)…Namely, this is a feedback of the DCM" and Page 10 via "where ηG and ξG can be regarded as the CCM and the DCM, respectively, as well as η and ξ defined in Equation (16). Also, the capture region regarding β can be defined…Therefore, the control problem results in the control of β, which is also regarded as the DCM…").
Therefore, it would have been obvious to one of ordinary skill in the art prior to the effective filing date of the given invention to modify the posture control method of Pratt in view of the eigensystem and feedback used to perform control of Yamamoto as both references are directed towards posture and stability control, and as such, implementing Yamamoto's eigensystem would've yielded predictable results and provided a representation of the controls for the same type of inverted pendulum model. Furthermore, Yamamoto also discloses that the research is extending Pratt's: "Pratt and Drakunov [19] discussed the case that the spatial manifold in which the COM moves is represented as 𝔃G = f(xG), where ƒ is a twice-differentiable function with respect to xG…" [Yamamoto Page 9].
However, Modified Pratt does not explicitly disclose the linearization of the eigenvectors around the origin.
Nevertheless, Morasso--who is directed towards the stabilization of a cart inverted pendulum--discloses: linearizes the set of (See at least Page 9 via 'Box 4' via "For t > ton carry out the internal simulation by integrating the linearized dynamical model of Equation 3, producing an un-delayed but approximated trajectory of the stick ˆθ=ˆθ(t);" and Page 4 via "…simulations considered in the results section use the non-linear model above, for stability analysis and for managing the alternation between on- and off-phases a linearized model is used, in the neighborhood of the origin, described by the following equations…" **Wherein the linearized dynamic model is integrated around the origin/stable manifold in order to perform stability analysis).
Therefore, it would have been obvious to one of ordinary skill in the art prior to the effective filing date of the given invention to modify Modified Pratt in view of the linearization around the origin in order to improve the stabilization: "…for the intermittent control policy the feedback control action operating in the on-phase is not intended to push the state toward the ideal equilibrium position, i.e., the origin of the phase space, but to drive the orbit as close as possible to the stable manifold in order to turn off the control action when and if such condition is reached" [Morasso Page 3].
Claims 4 is rejected under 35 U.S.C. 103 as being unpatentable over Pratt et. al. (2007 NPL, "Derivation and Application of a Conserved Orbital Energy for the Inverted Pendulum Bipedal Walking Model") and Yamamoto et. al. (2020 NPL, IDS, "Survey on Model-Based Biped Motion Control for Humanoid Robots") in view of Takenaka (US 20040044440 A1).
Regarding Claim 4, Modified Pratt discloses the posture control method according to Claim 1.
Furthermore, Pratt discloses: the conservation energy function (See at least Page 4653 via "We derive a new expression for a conserved quantity during single support, which we refer to in this paper simply as the “Orbital Energy”" and Equations (2) & (3); "where z = f(x) is the Center of Mass height as a function of the horizontal displacement from the foot to the Center of Mass…this expression for Orbital Energy allows us to determine where to step to achieve a next step velocity" and "where z = f(x) is the Center of Mass height as a function of the horizontal displacement from the foot to the Center of Mass, f′(x) is the derivative of f(x) with respect to x and g is the acceleration of gravity.")
However, modified Pratt does not explicitly disclose the parametric variable.
Nevertheless, Takenaka--who is directed towards gait pattern generating system of a legged mobile robot--discloses: wherein the (See at least ¶0357 via "The terminal divergent component induced by the leg motion is expressed by a function that inputs the gait parameters (in particular, the leg motion parameter and time parameter). Accordingly, if mapped data that shows the relationship between the gait parameters and the terminal divergent component induced by the leg motion, the volume of calculation will be decreased, although additional capacity of memory is needed…")
Therefore, it would have been obvious to one of ordinary skill in the art prior to the effective filing date of the given invention to set or express the orbital energy/conservation energy function using parametric variable(s), such as taught b Takenaka's gait motion that is represented using parameters, because representing robotic motion with parametric variable(s) as a way to describe the trajectories.
Claims 5 and 7 are rejected under 35 U.S.C. 103 as being unpatentable over Pratt et. al. (NPL, "Derivation and Application of a Conserved Orbital Energy for the Inverted Pendulum Bipedal Walking Model"), Yamamoto et. al. (2020 NPL, IDS, "Survey on Model-Based Biped Motion Control for Humanoid Robots"), and Morasso et. al. (2019 NPL, "Stabilization of a Cart Inverted Pendulum: Improving the Intermittent Feedback Strategy to Match the Limits of Human Performance") in view of Caron (2019 NPL, "Divergent Components of Motion").
Regarding Claim 5, Modified Pratt discloses the posture control method according to Claim 2.
Furthermore, although Morasso discloses linearization, Modified Pratt does not explicitly disclose, but Caron--who is directed towards Linear Inverted Pendulum Motion—discloses: Wherein the linearized set λ =
±
ω
'
of eigenvectors that is the convergent component and the divergent component is obtained from the following equation:
d
d
t
θ
θ
˙
=
0
1
ω
'
2
0
θ
θ
˙
(See at least Slide 9 via "The diagonalization of A" , state space Matrix A , and the eigenvalues).
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978
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Therefore, it would have been obvious to one of ordinary skill in the art prior to the effective filing date of the given invention to utilize any mathematical expression, including that of the claimed invention, which would have been an obvious design choice for one of ordinary skill in the art because it facilitates known mathematical means for deriving the linearized state-space equation of motion for a linear inverted pendulum, which includes the same state matrix form as the claim as shown in Matrix A as shown by Caron. Since the invention failed to provide novel or unexpected results from the usage of said claimed formula, use of any mathematical means, including that of the claimed invention, would be an obvious matter of design choice within the skill of the art. In addition, because both Modified Pratt and Caron are directed to inverted pendulum models, it would have been obvious for a person with ordinary skill in the art, at the time the invention was made, to have derived an equation to define the components of the linearized state space equation.
Regarding Claim 7, Modified Pratt discloses the posture control method according to Claim 2.
Furthermore, Caron discloses: wherein Kp is a gain, Kv is a gain,
θ
is a state quantity of an inverted pendulum expressed in a parametric variable,
θ
˙
is a time derivative of
θ
,
τ
θ
is an input to a system, and
ω
is a slope of the divergent component and is Kp/Kv, and wherein the control device performs the feedback on the basis of the following equation:
τ
θ
=
K
p
θ
+
K
v
θ
˙
=
K
p
θ
+
1
ω
θ
˙
(See at least Slide 8 via the linear feedback equation **Wherein Caron's
Δ
c
corresponds to the state quantity,
Δ
c
˙
corresponds to the derivative, and
Δ
u
corresponds to
τ
θ
. Furthermore Kp
θ
+
1
ω
θ
˙
.
is an algebraic rewritten expression of the same equation disclosed by Caron. Also see Slide 12 via "kv = kp/ω").
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992
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Therefore, it would have been obvious to one of ordinary skill in the art prior to the effective filing date of the given invention to modify Modified Pratt in view of Caron's defined expression of linear feedback control because both Modified Pratt and Caron are directed towards controlling an inverted pendulum model for biped robotic movement, and thus, the feedback is a predictable technique for stabilizing the inverted pendulum.
Claims 6 is rejected under 35 U.S.C. 103 as being unpatentable over Pratt et. al. (2007 NPL, "Derivation and Application of a Conserved Orbital Energy for the Inverted Pendulum Bipedal Walking Model") and Yamamoto et. al. (2020 NPL, IDS, "Survey on Model-Based Biped Motion Control for Humanoid Robots") in view of Zhao et. al. (2017 NPL, "Robust optimal planning and control of non-periodic bipedal locomotion with a centroidal momentum model").
Regarding Claim 6, Modified Pratt discloses the posture control method according to Claim 3.
However, Modified Pratt does not explicitly disclose, but Zhao--who is directed towards a theoretical method for planning and controlling agile bipedal locomotion--discloses: wherein
θ
is a state quantity of an
θ
˙
θ
is a gravitational acceleration
θ
Ω
θ
θ
˙
=
±
g
X
θ
C
θ
2
θ
=
±
Ω
θ
x
(See at least Equation 14 on Page 1216 and "where the phase-space asymptotic slope is defined as…" **Wherein Zhao discloses an equation defining the asymptote)
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848
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However, it is silent as to the specifics of applying mathematical formula for obtaining the asymptote as claimed.
Nevertheless, applying any mathematical formulae, including that of the claimed invention, would have been an obvious design choice for one of ordinary skill in the art because it facilitates known mathematical means for deriving a phase-space asymptotic slope, such as shown by Zhao. Since the invention failed to provide novel or unexpected results from the usage of said claimed formula, use of any mathematical means, including that of the claimed invention, would be an obvious matter of design choice within the skill of the art. In addition, because both modified Pratt and Zhao are directed towards inverted pendulum models, it would have been obvious for a person with ordinary skill in the art, at the time the invention was made, to have utilized an equation such as in Zhao, to achieve predictable result of obtaining an asymptote.
Claim 8 is rejected under 35 U.S.C. 103 as being unpatentable over Pratt et. al. (2007 NPL, "Derivation and Application of a Conserved Orbital Energy for the Inverted Pendulum Bipedal Walking Model") and Yamamoto et. al. (2020 NPL, IDS, "Survey on Model-Based Biped Motion Control for Humanoid Robots") in view of Caron (2019 NPL, "Divergent Components of Motion").
Regarding Claim 8, Modified Pratt discloses the posture control method according to Claim 3.
Furthermore, Caron discloses: wherein Kp is a gain, Kv is a gain,
θ
is a state quantity of an inverted pendulum expressed in a parametric variable,
θ
˙
is a time derivative of
θ
,
τ
θ
is an input to a system,
ω
is a slope of the divergent component and is Kp/Kv, and
Ω
(
θ
) is a function of
θ
, and wherein the control device performs the feedback on the basis of the following equation:
τ
θ
=
K
p
θ
+
K
v
θ
˙
=
K
p
θ
+
1
Ω
θ
θ
˙
(See at least Slide 8 via the linear feedback equation **Wherein Caron's
Δ
c
corresponds to the state quantity,
Δ
c
˙
corresponds to the derivative, and
Δ
u
corresponds to
τ
θ
. Furthermore
K
p
θ
+
1
Ω
θ
θ
˙
.
is an algebreic rewritten expression of the same equation disclosed by Caron Also see Slide 12 via "kv = kp/ω").
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Therefore, it would have been obvious to one of ordinary skill in the art prior to the effective filing date of the given invention to modify Modified Pratt in view of Caron's defined expression of linear feedback control because both Modified Pratt and Caron are directed towards controlling an inverted pendulum model for biped robotic movement, and thus, the feedback is a predictable technique for stabilizing the inverted pendulum.
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Caron (2019 NPL, “Linear Inverted Pendulum Model”)
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/K.R.D./Examiner, Art Unit 3657 /ABBY LIN/Supervisory Patent Examiner, Art Unit 3657
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