Real-time humanoid motion generation through ZMP manipulation based on inverted pendulum control
1. Paper overview
In one sentence: An inverted-pendulum approximation turns feasible ZMP references into whole-body joint motion, trading explicit full-body dynamics for a compact feedback pipeline demonstrated only in simulation. e01e02e03e05e06e07e08e12e14
| At a glance | What to know |
|---|---|
| Research problem | Source description How can a humanoid change motion online without solving its complete dynamics at every instant? The paper seeks responsive control from the current state, using the relationship between the center of gravity (COG) and zero moment point (ZMP) to reduce computational complexity. Its claims of agility concern computer simulations. e02e11 |
| Core mechanism | |
| A key reported result | Stepping under an impact disturbance: The authors report that the robot did not overturn during disturbed stepping; Figure 5 shows snapshots. Qualitative fall avoidance. Computer simulation of the Figure 4 humanoid: 30 DOF, 1270 mm height and 35 kg reported weight. No dataset split applies; impact parameters and repetition count are unspecified. No matched controller baseline or success-rate denominator is reported. Evidence for one simulated disturbance scenario, not a quantified robustness envelope or physical-robot result. e10e12 |
| Reading caution |
Core contributions
Figure 1. The ZMP plays the role of an equivalent pendulum support point in the reduced balance model. Original paper, p. 2 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Compare the pendulum on the left with the biped on the right. Both place a marked center of gravity above a support location. On the biped, follow the dashed line from x_G to x_ZMP on the horizontal line crossing the terrain. Section 2.1 supplies the mathematical meaning: approximate force and geometric equations relate horizontal COG acceleration to its displacement from the ZMP. Equations (3)–(5) also make the relation depend on vertical acceleration and COG height above the VHP. Section 2.3 then uses a referential ZMP to calculate COG acceleration, integrates it into a strict velocity reference, and passes that reference to the whole-body decomposer. e02e03e06e07e08e14
What it supports. The analogy provides a compact dynamical interface between balance planning and articulated motion. A support-point target determines a COG-motion reference under the approximation; the Jacobian and local joint controllers then turn that reference into joint motion. The drawing explains the model choice, while the numbered algorithm supplies the control stages.
Where the evidence stops. The biped cannot move its ZMP directly as the cart can move its support. The figure is a conceptual approximation, not a full-body dynamics model or a stability proof. It gives no measured computational cost or experimental accuracy.
2. Motivation
2.1 The problem and the proposed response
How can a humanoid change motion online without solving its complete dynamics at every instant? The paper seeks responsive control from the current state, using the relationship between the center of gravity (COG) and zero moment point (ZMP) to reduce computational complexity. Its claims of agility concern computer simulations. e02e11
2.2 What this reading follows
A humanoid cannot move its zero moment point as if it were a directly actuated cart. Sugihara, Nakamura and Inoue instead use that point as an intermediary: plan where support should act, derive a compatible center-of-gravity motion, and distribute the resulting velocity across joints. This reading follows the geometry and controller before examining the simulated impact test. The useful result is a concrete account of how reduced balance dynamics can drive an articulated body online. Its boundary is equally concrete: the source presents snapshots and tracking curves, but no measured runtime, controller ablation or physical-robot experiment. e01e02e03e05e06e07e08e12e14
3. Research context
We place the paper in the collection through its world–action interface. The catalog labels and the reading’s assessment are shown separately.
| Catalog dimension | Recorded classification |
|---|---|
| Major category | Foundational work |
| Architecture | Not applicable |
| Prediction paradigm | Not applicable |
| Quadrant | Not applicable |
3.1 Evidence-based assessment
Supports the recorded classification
The recorded foundational theory/planning and action-policy classification fits an analytic feedback-control paper. Architecture, prediction paradigm and quadrant are correctly marked not applicable: no learned world/action model is presented. Its four control blocks do not constitute evidence for a One Model or joint future/action-prediction architecture. e03e05e07e08e09
This is the collection’s architectural analysis, not a new related-work survey. Benchmark comparisons and their protocols appear in Section 6.
4. Problem formulation
4.1 Inputs and outputs
| Inputs | Outputs |
|---|---|
|
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4.2 Equations and their role
5. Method in detail
5.1 Why the desired velocity is not the command sent to the joints
Begin with the requested COG velocity. The planner uses an inverted-pendulum controller to choose a referential ZMP, then projects an infeasible choice back into the supporting polygon. That support target cannot be commanded directly to a legged robot. The manipulator first chooses vertical acceleration from vertical velocity error, then uses the current COG and referential ZMP in Eqs. (7)–(9) to determine horizontal acceleration. Integration produces the strict referential COG velocity. This intermediate differs from the original request because it is constructed to manipulate support through motion. The height-dependent factor links vertical and horizontal behavior, so vertical control is part of the balance calculation. The authors discuss hopping and running as possibilities, but their experiments do not establish those capabilities. e03e04e05e06e11
Figure 2. Uneven physical contacts become equivalent support points on a common horizontal plane. Original paper, p. 3 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Start at the marked COG, x_G, and trace each dashed ray through a real contact point p_i to its intersection p_i' with the VHP. The arrows continue along the COG–contact lines; these are not vertical projections. The drawing presents a cross-section, while the accompanying text forms the convex hull of all projected contacts on the plane. That hull supplies the supporting polygon used by the ZMP planner. If the requested ZMP falls outside it, the algorithm substitutes the nearest point inside. The VHP is a geometric construction for reasoning about support, not a replacement physical floor in the simulator. e03e04e05e11
What it supports. Contact geometry becomes an explicit constraint on the reduced controller. The method can discuss noncoplanar contact points using one planar feasible region, then constrain the balance reference before converting it into joint motion. This is the geometric bridge between the uneven-environment sketch and the pendulum model.
Where the evidence stops. The figure establishes the projection construction under the paper's force approximation. It does not display friction limits, actuator limits or a rough-terrain experiment, so membership in this polygon alone should not be read as a complete physical feasibility guarantee.
5.2 Why a supporting-foot convention matters to the COG Jacobian
The decomposition step must connect whole-body COG velocity to individual joint rates. First, the paper averages link COG Jacobians using link masses in the moving base frame. That result alone does not describe COG motion in the world, because joint motion can also move the base. Equations (15)–(16) account for a link held fixed in world coordinates, such as the supporting foot, and include its translational and rotational Jacobians before applying the base attitude. Next, the controller stacks COG and additional task constraints, separates prescribed joint motions, and solves the remaining system with a weighted pseudoinverse. Integrating those rates gives angle references for local actuators. The source leaves the weights and detailed controller configuration unspecified, so this derivation is more complete than its numerical reproduction recipe. e07e08
Figure 4. The simulation uses one articulated humanoid with 30 degrees of freedom. Original paper, p. 5 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Read the labels beside the skeleton as a model specification. The 30 total degrees of freedom are divided into 4 for the head, 14 for the arms and 12 for the legs; the height is 1270 mm and the source labels weight as 35 kg. These numbers identify the scale and articulation of the demonstrated system. Relate the many joints to the decomposer: the COG task alone does not uniquely select every joint rate, so prescribed joint motions and other constraints enter the stacked Jacobian system. The figure provides aggregate properties rather than the complete kinematic and inertial data needed to reconstruct that system. e07e08e10e11e14
What it supports. The paper's simulations exercise the controller on a many-joint humanoid, consistent with its motivation for a general COG Jacobian. However, this is one reported robot configuration. Its DOF count demonstrates the example's dimensionality, not measured speed or proof of generalization to every humanoid morphology.
Where the evidence stops. The figure does not provide individual link lengths, masses, COG locations, inertias, actuator models or simulator settings. Reproducing a similarly sized robot would be a declared reconstruction, not recovery of the exact source model.
5.3 How to read the impact result without turning a trace into a benchmark
The source's evaluation has three layers. Figure 4 identifies the simulated robot, Figure 5 illustrates disturbed stepping, and Figure 6 shows COG and ZMP trajectories. Read the right-hand plot in each axis pair as reference tracking within the proposed system, not a comparison with another controller. The authors' statement that the robot did not overturn is a qualitative outcome; it does not supply a success rate because no denominator is reported. Likewise, the time axes describe the motion, not the time required to compute a control update. Reader analysis: these layers establish a plausible simulation demonstration of the control chain, but they do not identify which component caused recovery. A reproduction should therefore add explicit disturbance parameters, aligned coordinate conventions and component controls rather than infer them from the curves. e10e12e13e14
5.4 Training and inference
During training
No learned representation, training data, fitted policy, frozen module or training loss is introduced. The method specifies analytic dynamics, kinematic Jacobians and feedback control; controller gains and pseudoinverse weights are implementation choices. e03e05e06e07e08
During inference
Here inference means online control: state feedback updates the ZMP/COG reference chain, and local actuators execute joint commands. There is no generated video, learned future-state rollout or inverse-dynamics network. Figure 3 sketches feedback, but its intermediate signs do not establish a complete executable controller. e06e08e09
5.5 Implementation flow
- Construct feasible support
Intersect each line from the COG through a real contact point with the VHP. Take the convex hull of the resulting equivalent contacts. This supporting polygon bounds the planned ZMP in the paper's approximate contact model. e04
- Plan the referential ZMP
An inverted-pendulum controller selects a ZMP reference to make COG velocity approach the requested velocity. PID and H-infinity control are examples, not an identified experimental configuration. Replace an outside reference with the nearest point in the supporting polygon. e05
- Generate a strict COG reference
Choose vertical acceleration using proportional velocity feedback, compute horizontal acceleration from the desired ZMP and current COG, then integrate. The resulting strict referential COG velocity differs from the original requested velocity: it is the intermediate motion command used to manipulate ZMP indirectly. e06
- Build the whole-body Jacobian
Average individual link COG Jacobians using link masses in base coordinates. Correct for translation and rotation of a link assumed fixed in world coordinates, such as the supporting foot, and rotate into the world frame. This yields the COG Jacobian relating joint rates to whole-body COG velocity. e07
- Resolve constraints and actuate
Stack COG and additional task-velocity constraints; separate prescribed joints from the remaining joints. Solve the reduced system with a weighted pseudoinverse, integrate joint rates into angle references, and let local actuators track them. The paper treats inertial effects as implicit at this local-control stage. e08
6. Experiments & results
This classical humanoid controller turns a desired center-of-gravity velocity into a feasible zero moment point, then into whole-body joint references. An inverted-pendulum approximation supplies the dynamics, while a constrained COG Jacobian distributes motion across joints. Simulated stepping survives an unspecified impact, but the paper provides no hardware validation, measured runtime or comparative error statistics.
The complete six-page source has six numbered figures and no quantitative results table or controlled ablation. Figure 4 reports robot configuration rather than comparative performance; Figures 5–6 provide a simulation sequence and trajectory diagnostics. This edition uses six original crops from Figures 1, 2, 4, 5 and 6, splitting Figure 6 into its X and Y panel pairs for readability. The Y pair serves as a diagnostic, not a newly claimed ablation. Figure 3 was inspected on page 4, but its joint-angle interface symbols are missing in the supplied PDF rendering; it is not selected as a final crop. Figures 1–2 illustrate the method, while the controller explanation remains grounded in Section 2.3 and its equations. Figure 3 also leaves its intermediate plus-sign conventions unresolved. Missing impact settings, error statistics and runtime measurements remain unresolved. e03e04e06e07e08e09e10e12e13e14
6.1 Read the original evidence
Figure 5. The reported impact test is illustrated by eight simulated stepping poses. Original paper, p. 6 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Read the strip from left to right as the paper's visual account of a stepping motion with an impact. The leg configurations and body posture change across the eight panels, while the robot remains upright in the shown frames. Section 3 supplies the essential interpretation: the authors say the robot did not overturn despite the disturbance. The strip itself has no impact arrow, frame timestamps, force trace or success criterion. Pair it with Figure 6 to see COG and ZMP behavior, but do not align a particular snapshot with a particular trajectory peak because the source gives no such correspondence. e10e12e13e14
What it supports. The visual supports the existence of a simulated disturbed-stepping demonstration and makes the authors' non-overturning report concrete. It is the strongest directly illustrated robustness example in the paper, but it remains a qualitative scenario rather than a measured success rate over repeated disturbances.
Where the evidence stops. Impact magnitude, direction, application point, duration and trial count are unspecified. These still images neither establish physical-robot recovery nor show a full animation, and they cannot define the controller's maximum recoverable disturbance.
Figure 6, two X-axis panels. The X plots distinguish COG motion from ZMP motion and show reference tracking. Original paper, p. 6 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. The left panel compares the solid centroid trace with the ZMP trace; the right panel compares referential ZMP with real ZMP. Read the legends separately because each panel compares a different pair of quantities. Both horizontal axes are labeled in milliseconds from 0 to 600, and the vertical axes give millimeters. The centroid changes relatively smoothly while the ZMP has sharp excursions. On the right, compare the two curves around those excursions and the subsequent return, rather than treating a peak position as an error value. Section 3 calls the tracking accurate, but the plot supplies no summarized error metric. e03e12e13e14
What it supports. The X traces are consistent with the intended division of roles: COG motion and support-point motion differ, while actual ZMP broadly follows its reference during the shown motion. Visible transient differences keep this a qualitative tracking observation. The figure reports position trajectories, not computational latency.
Where the evidence stops. The text notes a robot-base-coordinate transformation for ZMP without separately clarifying the COG frame convention. Do not subtract curves across panels to infer dynamics or an RMSE. No numerical accuracy threshold, repetition count or baseline controller is given.
6.2 Results and evaluation conditions
| Task & protocol | Reported result | Comparison & interpretation |
|---|---|---|
| Stepping under an impact disturbance Computer simulation of the Figure 4 humanoid: 30 DOF, 1270 mm height and 35 kg reported weight. No dataset split applies; impact parameters and repetition count are unspecified. | The authors report that the robot did not overturn during disturbed stepping; Figure 5 shows snapshots. Qualitative fall avoidance | No matched controller baseline or success-rate denominator is reported. Evidence for one simulated disturbance scenario, not a quantified robustness envelope or physical-robot result. e10e12 |
| ZMP reference tracking during disturbed stepping Figure 6 plots X and Y positions in millimeters against time axes labeled 0–600 ms; the text says ZMP is transformed into robot base coordinates. | The authors describe good accuracy; plotted curves broadly agree, with visible transient differences. No scalar tracking error is supplied. Visual agreement of referential and actual ZMP | Reference versus actual ZMP within the proposed system, not versus another method. The plots support a qualitative tracking diagnostic. They cannot establish an RMSE, statistical advantage or computation time. e13 |
| Online motion generation in simulation The same simulated humanoid; no train/test protocol. | Three-dimensional COG displacement on both feet, stepping, one-step-forward motion and walking are reported. Demonstrated motion repertoire | No comparative motion-generation experiment. The repertoire supports feasibility in simulation; superior agility and realtime efficiency are not measured quantitatively. e11e14 |
6.3 Ablations and diagnostic examples
Read component removals and qualitative examples within their stated evaluation conditions.
Figure 6, two Y-axis panels (tracking diagnostic). The Y plots expose transient support changes without isolating a controller component. Original paper, p. 6 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Use the left panel to follow the slower centroid path alongside the larger, sharper ZMP changes. Then move to the right panel and compare reference and actual ZMP directly. Preserve the different vertical scales: the left axis extends from −400 to 400 mm, while the right extends from −400 to 300 mm. Both time axes are labeled 0–600 ms. The closely following curves and short-lived differences are a tracking diagnostic for the demonstrated motion. No event markers identify which excursion corresponds to the imposed impact or a contact transition, so those causal assignments remain unresolved. e12e13e14
What it supports. The Y direction adds information that the X plots alone would miss: the shown motion includes substantial changes in support-related position and corresponding reference tracking. This strengthens the qualitative account of the simulated test, while leaving the size, cause and statistical reliability of tracking errors unquantified.
Where the evidence stops. This visual fills the diagnostic role; the paper contains no controlled ablation. The curves cannot isolate the benefit of the ZMP manipulator, supporting-polygon projection or local actuators. A matched component comparison would require new experiments.
7. Analysis & limitations
7.1 What the evidence leaves open
The reduced model does not explicitly account for all inertial forces beyond gravity in control. Local joint control is said to handle these effects implicitly; this is not a full-body dynamics guarantee. e02e08
Running, hopping and adaptation to rough terrain are discussed as possibilities enabled by vertical control, not demonstrated outcomes of the reported simulations. e06e11
There is no quantitative results table, ablation, hardware test, timing benchmark or uncertainty estimate. Disturbance magnitude, contact parameters and controller settings are not specified sufficiently to establish a repeatable robustness comparison. e05e06e08e12e14
7.2 Questions for discussion
- Under what contact and motion conditions does the inverted-pendulum approximation cease to produce useful joint references?
- How much of disturbance recovery comes from indirect ZMP control versus the unspecified local joint controllers?
8. Reproducibility audit
8.1 Requirements and known gaps
A reproduction requires link geometry, per-link masses and COGs, a fixed-contact convention, task constraints, local actuator dynamics, integration settings, gains and pseudoinverse weights. Figure 4 gives only an overall structure and aggregate size/weight, not a complete robot or simulator specification. e07e08e10e14
Reader-proposed checks: validate the world-frame COG Jacobian against finite differences while holding the support foot fixed; then compare disturbed stepping with full indirect ZMP control against a matched direct COG-velocity command. Record constraint residuals, falls and ZMP error, declaring all unspecified implementation choices. e06e07e08e12e13
8.2 Proposed reproduction checks
The following checks are proposals motivated by the paper. They have not been run as part of this reading.
Check 1: Check the support-fixed COG Jacobian before testing recovery
Reader-proposed, not executed: construct a robot with fully declared link parameters, hold a chosen support foot fixed, and compare COG velocities predicted by Eq. (16) with finite differences of forward kinematics after joint perturbations. Use the uncorrected base-frame mass-weighted Jacobian as a control. Sweep perturbation sizes and configurations; log world-frame COG error, support-foot drift and stacked task-constraint residuals. Away from numerical degeneracy, the corrected prediction should approach the finite-difference result as the step shrinks. Persistent mismatch would falsify the implemented frame/sign handling before any claim about disturbance rejection. Publish all reconstruction choices because Figure 4 alone does not specify the robot. e07e08e10
Check 2: Isolate the contribution of indirect ZMP control during impact
Reader-proposed, not executed: compare the complete reference-ZMP-to-strict-COG pipeline with a control that sends the requested COG velocity directly to the same constrained decomposer. Hold the robot, nominal task, local actuators, integration step and common settings fixed. Sweep declared impact directions, impulses and stepping phases, including a no-impact condition. Record falls under a predeclared criterion, task deviation, and actual-versus-feasible-reference ZMP error in one common frame. Larger recoverable disturbances or lower tracking error for the complete pipeline would support a specific contribution from indirect ZMP control; no consistent difference would weaken that attribution. Report separate gain-sensitivity runs, since the source does not identify its gains or impact settings. e05e06e08e12e13e14
8.3 Reading coverage
Visual audit: Visually inspected all six PDF pages: title, authors, affiliations and motivation on p. 1; approximation, Eqs. (1)–(5) and Figure 1 on p. 2; VHP geometry, planning and Eqs. (6)–(10) on p. 3; Figure 3, COG Jacobian and constraints on p. 4; remaining decomposition equations, local control, robot specification, simulations and conclusion on p. 5; Figures 5–6 and References on p. 6. Inspected a magnified original PDF excerpt of Eqs. (3)–(5), confirming the double-dot acceleration symbols and the vertical-acceleration/height ratio. All six selected final crops were opened and inspected after extraction: Figure 1, Figure 2, Figure 4, Figure 5 and both axis pairs of Figure 6. Narrow diagrams and plots were rendered at higher DPI directly from the PDF. The incomplete joint-angle interface symbols in Figure 3 cannot be recovered from this source rendering; Figure 1 supplies the selected pendulum-method visual instead. Figure 3 remains supporting source evidence, and its intermediate plus signs were cross-checked against the algorithm without reconstructing missing labels. All pages supporting retained method, numerical, evaluation and reproduction claims are included. No table or appendix exists in this artifact. No external media, code, separate supplement or publisher edition was inspected.
PDF pages inspected for this edition: 1, 2, 3, 4, 5, 6. Appendix coverage: not present.
Original figures and tables remain the work of the source’s authors. Extractions preserve their scientific content; any HTML wrapper layout is disclosed with each figure. The surrounding reading notes are our own.
Text reading scope & known omissions
- Abstract (PDF p. 1)
- 1 Introduction (PDF pp. 1–2)
- 2 Realtime Motion Generation; 2.1 The Principle of Legged Motion and Inverted Pendulum (PDF p. 2)
- 2.2 The VHP and The Supporting Polygon (PDF pp. 2–3)
- 2.3 The Algorithm, all four steps and Eqs. (6)–(20) (PDF pp. 3–5)
- 3 Simulation (PDF p. 5, with Figures 5–6 on p. 6)
- 4 Conclusion (PDF p. 5)
- References (PDF p. 6)
Outside the original text pass
- PDF font mapping and two-column reading order can affect equation glyphs and spacing. This extraction is not a verified mathematical transcription; equations, figures and tables still require direct PDF inspection.
- The retained file is the complete author-hosted six-page paper version. It omits the IEEE proceedings masthead and printed page labels; publication identity is linked through the author publication list and the verified IEEE DOI.
- External code, datasets, videos and separate supplements were not retrieved or verified.
- Identity notes: PDF p. 1 confirms the observed title and all three catalog authors. The catalog uses “Real-time” and sentence case; this artifact uses “Realtime” and title case. The supplied acquisition record identifies an author-hosted ICRA 2002 paper associated with DOI 10.1109/ROBOT.2002.1014740, not a byte-identical IEEE proceedings PDF. No revision number or date is printed in this artifact; version identity is bounded by the supplied PDF hash.
- Both supplied text chunks and all six PDF pages were read. Figures 1–6 were visually inspected; no tables or appendix are present. Figure 3 has incomplete joint-angle labels in the supplied PDF rendering and ambiguous intermediate plus-sign junctions; the numbered algorithm and equations supply the interpretable method. The illustrated edition uses Figure 1 as a legible method visual in place of Figure 3.
- No external source, code, dataset, video or separate supplement was inspected, and no experiment was reproduced.
The visual audit above records the subsequent illustrated pass.
8.4 Traceable evidence
e01PDF p. 1, title and author/affiliation block
Observed title uses “Realtime”; authors are Tomomichi Sugihara, Yoshihiko Nakamura and Hirochika Inoue. Affiliations identify the University of Tokyo department and CREST/JST.
Go to primary source ↓e02PDF pp. 1–2, Abstract and Section 1 Introduction
Motivates responsive motion generation using low-dimensional dynamics, claims general kinematics/DOF compatibility, and acknowledges that inertial forces other than gravity are not explicitly considered in control.
Go to primary source ↓e03PDF p. 2, Section 2.1, Eqs. (1)–(5), Figure 1
An approximate resultant-force model yields inverted-pendulum-like horizontal COG acceleration about ZMP; omega_G depends on vertical acceleration and COG height above the VHP.
Go to primary source ↓e04PDF pp. 2–3, Section 2.2, Figure 2
Lines connecting COG and real contact points intersect the VHP at equivalent contacts; their convex hull is the supporting polygon.
Go to primary source ↓e05PDF p. 3, Section 2.3, step 1 Referential ZMP Planning
An inverted-pendulum controller chooses ZMP to regulate COG velocity; an infeasible reference is replaced by the nearest point in the supporting polygon. PID and H-infinity controllers are examples.
Go to primary source ↓e06PDF p. 3, Section 2.3, step 2 ZMP manipulation, Eqs. (6)–(9)
Vertical proportional velocity feedback and referential pendulum equations yield COG acceleration; integration produces a strict velocity reference distinct from the original desired velocity. Hopping/running are proposed possibilities.
Go to primary source ↓e07PDF pp. 3–4, Section 2.3, step 3, Eqs. (10)–(16)
Defines the COG Jacobian, obtains its base-frame form as a mass-weighted sum of link Jacobians, and corrects it using a world-fixed link and base attitude.
Go to primary source ↓e08PDF pp. 4–5, Section 2.3, joint/task constraints, Eqs. (17)–(20), step 4
Stacks COG and other velocity constraints, separates prescribed joints, solves with a weighted pseudoinverse and integrates joint rates. Local actuators track angle references.
Go to primary source ↓e09PDF p. 4, Figure 3 and caption; p. 3, step 2/Eqs. (6)–(9); p. 5, step 4
The block chart depicts planner, manipulator, decomposer and actuator feedback. Its intermediate junctions carry plus signs and joint-angle labels are incomplete in the supplied rendering; the text provides the acceleration/integration and angle-tracking descriptions.
Go to primary source ↓e10PDF p. 5, Figure 4 and caption
Robot specification: 30 DOF, comprising 4 for the head, 14 for arms and 12 for legs; height 1270 mm; weight 35 kg. The figure does not supply full link parameters.
Go to primary source ↓e11PDF p. 5, Section 3 Simulation and Section 4 Conclusion
Reports COG displacement on both feet, stepping, one-step-forward motion and walking in a simulator; concludes usefulness from computer simulations.
Go to primary source ↓e12PDF p. 5, Section 3 disturbance paragraph; PDF p. 6, Figure 5 and caption
Describes stepping with an impact and states the robot did not overturn. Eight simulation snapshots are shown; no impact magnitude, frame timestamps or trial statistics are supplied.
Go to primary source ↓e13PDF p. 5, Section 3 final paragraph; PDF p. 6, Figure 6, all four panels
COG/ZMP and referential/actual ZMP are plotted for X and Y in mm against axes labeled 0–600 ms. Text notes base-coordinate transformation of ZMP and claims good tracking accuracy, without scalar error statistics.
Go to primary source ↓e14PDF pp. 5–6, complete Section 3, Section 4 and Figures 4–6
Evaluation consists of simulation descriptions, robot properties, snapshots and trajectories. No quantitative benchmark table, controlled ablation, measured runtime, computing hardware, statistical uncertainty or physical deployment is reported.
Go to primary source ↓8.5 Primary sources
Realtime Humanoid Motion Generation through ZMP Manipulation based on Inverted Pendulum Control ↗
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