A master’s engineering dissertation has examined two central challenges in the development of the biped humanoid robot: stable walking and recovery from external pushes. The work, titled Gait Planning and Anti-Push Algorithm of Biped Humanoid Robot, was completed at Harbin Institute of Technology, Shenzhen, by Yang Jin under the supervision of Associate Professor Li Yanjie. The research combines kinematic modeling, linear inverted pendulum methods, simulation with a robotics operating system and V-REP, physical testing on a small biped humanoid robot platform, and a capture-point-based anti-push framework. The dissertation reports progress toward a more stable gait for a small humanoid robot and a simulation-validated approach for push recovery.
1. Research Context and Significance
The humanoid robot has moved from laboratory curiosity to a platform with growing relevance in service, logistics, inspection, disaster response, and human-centered environments. Among mobile robot forms, the biped humanoid robot is especially attractive because its two-legged structure can potentially navigate spaces designed for people, including stairs, doors, and uneven indoor terrain. However, the same structure that gives the humanoid robot its flexibility also creates difficult control problems. A biped humanoid robot must coordinate many joints, maintain balance under gravity, handle foot-ground impacts, and adapt to changes in surface friction and external forces.
The dissertation places its work within this context. It notes that while theoretical progress has been made in gait planning, many small biped humanoid robot products still lack reliable gait algorithms and environmental adaptation. In practical use, a humanoid robot may face hard floors, carpets, rubber mats, and unexpected pushes. Without a robust gait planner and a push recovery strategy, the humanoid robot can move slowly, fall easily, or fail to recover after a disturbance. The research therefore aims to improve gait generation for a small biped humanoid robot and to explore anti-push control through simulation.
The motivation is not only academic. A stable biped humanoid robot could support tasks in homes, offices, hospitals, and outdoor service roles. It could also operate in dangerous environments where human presence is risky. The dissertation argues that gait planning and anti-push capability are core competencies for any humanoid robot expected to work around people. A humanoid robot that can walk reliably and respond to pushes would be more useful, safer, and more autonomous.
2. Global and Domestic Research Landscape for the Humanoid Robot
The dissertation reviews international and domestic research on the biped humanoid robot. It divides the landscape into leading programs in the United States and Japan, secondary efforts in Korea, France, and Germany, and a rapidly developing but still younger Chinese research base. The review shows that the humanoid robot has benefited from decades of iterative hardware and software development, yet many challenges remain in dynamic stability and disturbance rejection.
2.1 United States Research on the Biped Humanoid Robot
The United States is described as an early leader in biped humanoid robot research. In the early 1990s, the MIT Leg Laboratory developed the Planar Biped, which could run, jump, and climb steps. The laboratory also produced the 3D Biped, a more advanced humanoid robot capable of running and jumping motions. These platforms helped establish dynamic walking and running concepts that continue to influence humanoid robot control.
Boston Dynamics later became a major force in legged robotics. The company’s BigDog quadruped demonstrated strong balance and locomotion over rough terrain. Boston Dynamics then developed PETMAN and Atlas, two humanoid robot platforms with hydraulic actuation and impressive whole-body motion. PETMAN was reported as approximately 1.75 meters tall and 80 kilograms, with a walking speed that could reach 7 km/h. Atlas extended this work with natural-looking gait, rough-terrain walking, snow walking, jumping, and even backflips. The dissertation notes that Atlas can respond to external pushes and adjust posture to avoid falling, although the public record does not fully disclose its gait planning method.
Other U.S. institutions have also contributed. The University of California, Berkeley, and Carnegie Mellon University developed ATRIAS, a biped humanoid robot designed for uneven terrain. ATRIAS was reported with a step length of 30 to 65 centimeters, a step height of 22 centimeters, and an average walking speed of 0.6 meters per second. Agility Robotics introduced Cassie, a biped humanoid robot inspired by an ostrich, and later Digit, which added arms and lidar for environmental sensing. These platforms use high-performance electric motors, making them compact and agile. The dissertation observes that Cassie and Digit represent important steps toward humanoid robot applications in homes and other human environments.
2.2 Japanese Research and the Humanoid Robot
Japan has one of the longest continuous traditions in biped humanoid robot research. Waseda University began work in 1968 and produced the WL-5 humanoid robot in 1971. The WL series continued for decades, leading to WL-16IV, a hydraulically driven humanoid robot capable of indoor and outdoor walking. In 2009, Waseda University introduced KOBIAN, described as the world’s first humanoid robot able to interact emotionally through facial expressions and gestures.
Honda’s humanoid robot program began in the 1990s and produced the P series. The P2 humanoid robot, introduced in 1996, was the world’s first human-like biped walking robot. The P3 humanoid robot followed in 1997 with a height of 1.6 meters and a weight of about 130 kilograms, pursuing miniaturization and weight reduction. The E series, with versions E0 through E6, built technical foundations in control and gait. Honda then introduced ASIMO in 2000. Over three major generations, ASIMO became capable of walking, running, climbing stairs, kicking a ball, opening a bottle, and pouring tea. The third-generation ASIMO was reported at 130 centimeters tall, 48 kilograms, a walking speed of 9 km/h, and 57 degrees of freedom.
Japan’s National Institute of Advanced Industrial Science and Technology developed the HRP series. HRP-4C, introduced in 2009, was 1.58 meters tall and weighed 43 kilograms, with facial expression capabilities. It was positioned as an entertainment humanoid robot rather than a commercial product. Smaller Japanese humanoid robot platforms also emerged. Sony’s SDR-4X, released in 2002, had 38 degrees of freedom and could walk and perform dance motions. Tomy’s i-sobot, released in 2007, was only 16.5 centimeters tall and weighed 350 grams, yet could perform many actions, walk on two legs, and play voice audio. These products showed the potential of small humanoid robot platforms, although their balance and disturbance rejection remained limited.
2.3 Other National Programs and the Humanoid Robot
Korea has become prominent in small biped humanoid robot development. Robotis released Darwin-OP, a platform for developers that uses vision for object tracking and can walk at about 20 centimeters per second with a stepping frequency of four steps per second. Hitec developed Robonova-1 and Robonova-2, also aimed at developers and enthusiasts. These humanoid robot platforms have been widely used in education and research.
France’s Aldebaran Robotics, later acquired by SoftBank, developed NAO, a 58-centimeter-tall humanoid robot weighing 5.4 kilograms and supporting programming in C, Python, JavaScript, and Java. Germany’s Technical University of Munich developed Lola, a 25-degree-of-freedom humanoid robot with a height of 180 centimeters, a weight of 55 kilograms, and a walking speed of 2.4 km/h. Lola was designed for walking on less even ground using electric motors.
2.4 Chinese Research on the Humanoid Robot
China’s humanoid robot research started later but has developed quickly, with universities and research institutes playing a leading role. Harbin Institute of Technology developed HIT-III in 1985, a 12-degree-of-freedom humanoid robot capable of biped walking. In 2004, the university introduced GoRoBoT-II, a 35-kilogram, 0.89-meter-tall humanoid robot with both legged and wheeled mobility. GoRoBoT-III followed in 2012, with a height of 1.58 meters, 70 degrees of freedom, and human-proportioned head and arms.
Tsinghua University released THBIP in 2002, a 1.7-meter-tall, 130-kilogram humanoid robot capable of stair climbing. Beijing Institute of Technology introduced BRH-II in 2005, a 1.6-meter-tall, 63-kilogram humanoid robot with motion capture functions. Tsinghua’s Stepper was 0.44 meters tall and could walk at 3.6 kilometers per hour. More recently, Chinese companies have entered the field. Ability Storm developed the Everest series for education, UBTECH developed the Alpha series for education and entertainment, and UBTECH introduced Walker, a larger biped humanoid robot capable of walking, kicking a ball, and climbing stairs. The dissertation notes that domestic humanoid robot products still generally lack the dynamic gait and anti-push capabilities seen in leading international platforms.
3. Kinematics and Inverted Pendulum Foundations
The dissertation builds its gait planner on kinematic modeling and the linear inverted pendulum model. These foundations allow the humanoid robot’s center of mass and foot trajectories to be converted into joint angles. The approach is chosen because the linear inverted pendulum offers a simpler mathematical structure than a full nonlinear model while still capturing essential dynamic walking behavior.
3.1 Inverse Kinematics for the Humanoid Robot
Inverse kinematics solves the leg joint angles from a desired torso pose and foot pose. The humanoid robot model has two kinematic chains, one for the left leg and one for the right leg. Each chain contains six joints, labeled from LEG_J0 to LEG_J5. By providing the starting pose and ending pose of a chain, the controller can compute the joint values needed to place the ankle or torso as desired.
The dissertation uses an analytical method for inverse kinematics. It defines the hip position relative to the torso, the distance from hip to ankle, and the thigh and shank lengths. With the cosine law, the knee angle is obtained. Using the sine law and geometric relations, the ankle pitch and roll angles are derived. The remaining joint angles are found by expanding the rotation matrix equation and solving for each angle. The same procedure applies to the left leg and the right leg. The result is a set of joint angles that can be sent to the humanoid robot’s servos.
3.2 Forward Kinematics for the Humanoid Robot
Forward kinematics calculates the pose of a link from known joint angles. For the biped humanoid robot, given the six joint angles in a leg chain and the torso or ankle pose, forward kinematics can determine the opposite end pose. The dissertation expresses this through homogeneous transformation matrices. The ankle frame relative to the torso frame is obtained by multiplying the transformations along the chain. Conversely, the torso relative to the ankle is obtained by inverting the result. Forward kinematics is used to estimate the humanoid robot’s center of mass and foot positions from measured joint angles, which is important for simulation monitoring and real-time feedback.
3.3 Linear Inverted Pendulum Model
The linear inverted pendulum model assumes that the humanoid robot’s mass is concentrated at the center of mass, the legs are massless, the contact point can rotate, and the center of mass height remains constant. Under these assumptions, the horizontal motion of the center of mass follows a simple second-order differential equation. The dissertation presents the solution for position and velocity as hyperbolic functions of time. The model’s time constant depends on gravity and the center of mass height. This linear inverted pendulum model becomes the core tool for planning the humanoid robot’s center of mass trajectory in both the coronal and sagittal planes.
4. Gait Planning Method for the Biped Humanoid Robot
The dissertation constructs a 20-degree-of-freedom humanoid robot model for gait planning. The model includes a torso, two legs, and a head, with each leg having six joints. The main focus is on the 12 leg joints because they determine walking. Head and arm joints are fixed during the gait experiments, as their influence on the center of mass trajectory is treated as secondary in this study.
4.1 Simulation Model and Degrees of Freedom
The humanoid robot model is simplified by treating the center of mass as a mass point and the ground contact point as the support point. The walking motion is decomposed into the coronal plane and the sagittal plane. In the coronal plane, the humanoid robot’s center of mass moves laterally between the left and right feet. In the sagittal plane, the center of mass moves forward and backward. The vertical direction is planned as a constant height for the center of mass. This decomposition makes it possible to apply the linear inverted pendulum model separately in each plane.
4.2 Stance Phase Planning
During the stance phase, one leg supports the humanoid robot while the other leg swings. The dissertation assumes that at least one foot is always on the ground and neglects double support transitions for planning purposes. For the coronal plane, the support foot center is treated as the inverted pendulum pivot. The center of mass moves from one side to the other with a periodic lateral motion. The initial velocity for each half-cycle is derived from the step width and the walking period. The resulting trajectory resembles a smooth oscillatory curve around the center line.
For the sagittal plane, the center of mass advances by half of the step length during each stance phase. Using the linear inverted pendulum solution, the initial velocity is computed from the step length and the half-period. The forward center of mass trajectory is then generated. The vertical center of mass height is kept constant. Together, these trajectories define the desired center of mass motion for the humanoid robot during walking.
4.3 Swing Phase Planning
The swing phase plans the motion of the non-supporting leg. In the coronal plane, the foot separation is kept constant, so no lateral displacement is planned for the swing foot. In the sagittal plane, the swing foot moves from behind the body to in front of the body over half of the walking period. The dissertation uses a sinusoidal function for the forward swing trajectory. In the vertical direction, the swing foot lifts to a maximum height and then returns to the ground. The original vertical trajectory is also sinusoidal, with the foot height starting at zero, reaching a maximum at mid-swing, and returning to zero at the end of the swing phase.
4.4 Simulation Environment and Results
The simulation environment is built on Ubuntu 16.04 using the Robot Operating System and V-REP. The Robot Operating System provides a framework for node-based control and message passing, while V-REP supplies a lightweight robotics simulator with kinematics, collision detection, and sensor simulation. A TALOS humanoid robot model is imported into V-REP. The model is 65 centimeters tall, weighs 5.386 kilograms, and has six degrees of freedom per leg. The center of mass height is 0.36 meters. The walking cycle is set to 1.6 seconds, the foot distance is 0.132 meters, and the sampling period is 20 milliseconds. These values are used consistently in the simulation and physical experiments.
| Parameter | Value |
|---|---|
| Overall height of the humanoid robot | 0.65 m |
| Overall weight | 5.386 kg |
| Thigh length | 0.136 m |
| Shank length | 0.136 m |
| Foot length | 0.16 m |
| Foot width | 0.14 m |
| Foot mass | 0.15 kg |
| Center of mass height | 0.36 m |
| Degrees of freedom per leg | 6 |
| Total degrees of freedom in the model | 20 |
| Walking cycle | 1.6 s |
| Foot distance | 0.132 m |
| Sampling period | 20 ms |
The simulation produces left-leg and right-leg joint angle curves from the planned center of mass and foot trajectories. The humanoid robot walks in the simulator by following these joint angles. The dissertation observes that the first simulation is broadly stable, but the center of mass changes sharply when the swing foot lands. This sharp change suggests that the impact at touchdown affects stability. The original swing foot height trajectory does not account for the ground impact, so the dissertation improves the swing foot trajectory.
4.5 Swing Foot Trajectory Improvement
To reduce landing impact, the dissertation replaces the second half of the original sinusoidal vertical trajectory with a smoother segment. The improved piecewise function keeps a fast lift-off slope and uses a gentler landing slope. The modification is intended to reduce the foot’s vertical velocity at touchdown, thereby reducing the impulse transmitted to the humanoid robot’s center of mass. In the simulation, the improved trajectory produces a higher center of mass minimum and a smoother center of mass height profile compared with the original trajectory. This indicates that the landing impact is smaller and the humanoid robot’s motion is closer to the planned constant-height behavior. The improved gait planning method is then used for physical experiments.
5. Physical Validation and Gait Algorithm Refinement
The dissertation validates the gait algorithm on a physical TALOS humanoid robot platform. The hardware parameters match the simulation model, which simplifies the transfer from simulation to reality. The platform can report joint angles in real time, allowing the center of mass position to be estimated through forward kinematics. In the physical experiments, arm components are omitted because arm swing is not modeled, and only leg joints are controlled. The goal is to determine whether the simulation gait remains stable on real hardware and across different ground surfaces.
5.1 Hardware Platform and Hard-Surface Tests
The first physical tests are performed on a flat, smooth, hard tabletop. The humanoid robot uses the joint angles generated by the linear inverted pendulum gait planner. The dissertation reports that the humanoid robot can walk stably under this condition. Key frames captured from the front and side show the humanoid robot stepping forward, shifting its center of mass toward the support leg, lifting the swing leg, and placing it forward. This confirms that the planned gait can be executed by the physical humanoid robot.
5.2 Multi-Surface Walking Tests
To test robustness, the gait algorithm is evaluated on a rubber mat and a hard carpet in addition to the hard tabletop. The humanoid robot walks on these surfaces using the same gait planner. The dissertation reports stable walking on all three surfaces. The center of mass trajectory in the coronal plane is compared with the planned trajectory. After the first step, the measured center of mass motion is smooth and closely follows the planned trajectory. The first step shows a larger deviation, but steady-state walking matches the planning. This result supports the reliability of the linear inverted pendulum gait method for a small biped humanoid robot on common indoor surfaces.
5.3 Disturbance Behavior Without Anti-Push Control
Before developing the anti-push algorithm, the dissertation tests the humanoid robot’s natural disturbance response. In simulation, a small lateral push is applied during walking. The push is set to 3 N along one horizontal direction and 4 N along another, applied at 2.2 seconds. The center of mass trajectory in the coronal plane deviates after the push and then returns to a periodic pattern after about two walking cycles, although the walking direction shifts. The sagittal trajectory also becomes irregular for a period and then resumes cyclical motion with a different pattern. The height trajectory shows a sharp change after the push and then recovers. These results show that the linear inverted pendulum gait has some passive robustness, but it is not sufficient for large disturbances. The dissertation notes that without anti-push control, a 10 N force during single support can cause the humanoid robot to fall.
| Method | Core idea | Role in the dissertation |
|---|---|---|
| Zero moment point | Keep the zero moment point inside the support polygon | Reviewed as a traditional stability criterion |
| Linear inverted pendulum model | Plan center of mass motion using a linearized pendulum | Chosen as the gait planning foundation |
| Central pattern generator | Use neural oscillators to produce rhythmic joint signals | Reviewed as a bio-inspired alternative |
| Fully dynamic stability control | Control height, posture, and velocity without a fixed stability index | Reviewed in the context of dynamic running and jumping |
| Capture point | Choose a step location to dissipate orbital energy | Used for anti-push control in simulation |
6. Anti-Push Control Based on Capture Point and Orbital Energy
The anti-push portion of the dissertation addresses the problem of a humanoid robot losing balance after an external push. The core idea is that a push increases the humanoid robot’s orbital energy. If the humanoid robot can take a step to a suitable location, it can dissipate that excess energy and return to a stable state. The capture point is the foot placement that allows the humanoid robot to stop or recover. The dissertation applies capture point theory to both stationary and moving humanoid robot states and validates the approach in simulation.
6.1 Push Factors and Definitions
The dissertation analyzes push factors including direction, onset time, duration, and magnitude. In the simplified model, the push is treated as a short-duration force that acts on the center of mass and produces an instantaneous change in momentum. The push direction is horizontal, with no vertical component in the main analysis. A push that significantly changes the humanoid robot’s momentum is called an impact force. The central problem is how to keep the humanoid robot balanced and return it to its prior state after such an impact.
The dissertation defines several concepts. The capture point is the foot placement that allows the humanoid robot to remain stable after a push. The capture state is the desired stable state. Orbital energy is the sum of kinetic energy and a fictitious potential energy in the inverted pendulum model. When the center of mass cannot pass a potential energy peak, its motion reverses. When it has enough energy, it passes the peak. The orbital energy remains constant in the ideal model, which makes it useful for detecting disturbances and planning recovery.
6.2 Capture Point for a Stationary Humanoid Robot
For a stationary humanoid robot, orbital energy is initially zero. After a push, orbital energy increases. To return orbital energy to zero, the humanoid robot must step to a capture point. The dissertation derives the capture point from the orbital energy equation. If the push gives the center of mass a velocity, the capture point lies ahead of the center of mass in the direction of motion. When stepping time is considered, the center of mass continues to move under gravity during the step, so the capture point changes. For a stationary start, the capture point can be expressed as the initial center of mass position plus a term that grows exponentially with the stepping time. This gives a practical way to choose a foot placement after a push.
6.3 Capture Point in Motion
The dissertation extends capture point analysis from a stationary humanoid robot to a moving one. Motion includes both stepping in place and walking forward. The forward and lateral cases are treated similarly, so the discussion focuses on forward motion. A disturbance is detected by monitoring orbital energy. Under normal walking, orbital energy should remain close to a reference value. When the difference between the current orbital energy and the normal value exceeds a threshold, the humanoid robot is considered to have been pushed. The current center of mass velocity and position become the inputs to the anti-push controller.
6.4 Walking Phase and Energy Adjustment
The walking cycle is divided into an acceleration phase and a deceleration phase. In the acceleration phase, the center of mass moves away from the support leg, and its acceleration is in the same direction as its motion. In the deceleration phase, the center of mass moves toward the support leg, and its acceleration opposes its motion. The dissertation uses orbital energy equations for both phases. When the humanoid robot is pushed, the orbital energy after the push is higher than normal. To bring the orbital energy back to the normal value, the acceleration distance should be shortened and the deceleration distance should be lengthened. In practical terms, the humanoid robot can adjust its step timing and foot placement. A shorter stepping time reduces the acceleration distance. A farther foot placement increases the deceleration distance. The combination can restore the desired orbital energy in one step if the required foot placement is within reach.
6.5 Anti-Push Control Algorithm
The dissertation outlines an anti-push control algorithm for a moving humanoid robot. The algorithm uses measured or estimated center of mass position and velocity as inputs. It computes the switching point between acceleration and deceleration, the initial velocity for the next step, the required deceleration distance, and the desired foot placement. If the desired foot placement is within the humanoid robot’s reachable range, the humanoid robot steps to that point and can recover in one step. If the desired placement exceeds the maximum reachable distance, the algorithm sets the step to the maximum allowed distance. If the humanoid robot remains standing after that step, the controller updates the state and repeats the process. If the humanoid robot falls, recovery ends. The algorithm therefore attempts to recover when possible and degrades gracefully when the push is too large.
- Read the center of mass position and velocity at the moment of disturbance.
- Compute the acceleration-deceleration switching point and the initial velocity for the next step.
- Compute the required deceleration distance from the orbital energy equation.
- Compute the desired foot placement by combining the switching point and the deceleration distance.
- Check whether the desired foot placement exceeds the maximum reachable distance.
- Use the desired foot placement if it is reachable, or use the maximum reachable distance otherwise.
- If the humanoid robot remains standing after the step, update the state and repeat the recovery process.
7. Simulation Results for Anti-Push Recovery and Fall Conditions
The anti-push controller is added to the real-time gait control system in simulation. The system monitors energy changes, detects a push when the energy difference exceeds a threshold, switches from the normal gait planner to the anti-push planner, and generates new center of mass and foot trajectories. For a humanoid robot stepping in place, the total orbital energy is not zero because the center of mass moves in the lateral direction. However, the forward direction can still be analyzed separately. The capture point in the forward direction and the recovery point in the lateral direction are combined to produce a foot placement in the horizontal plane.
In one simulation, the humanoid robot is stepping in place and receives a push of 30 N along one horizontal direction and 40 N along another at 1.35 seconds. The stepping time is set to 0.6 seconds. The anti-push algorithm computes the recovery foot placement. The center of mass trajectories in the sagittal, coronal, and vertical directions show that the humanoid robot deviates after the push, takes a recovery step, and returns to the stepping-in-place state. The dissertation presents this as evidence that the capture-point and orbital-energy method can restore balance for a moving humanoid robot under a moderate push.
A second simulation tests a stronger push under the same stepping time. The push is set to 30 N along one direction and 150 N along another at 1.35 seconds. In this case, the humanoid robot cannot reach the required capture point within the allowed stepping time, and it falls. The center of mass trajectories show a loss of balance in the coronal and vertical directions. This result illustrates the physical limits of the anti-push method. The humanoid robot’s leg length, joint speed, servo torque, and stepping time all constrain the maximum recoverable push.
| Scenario | Push setting | Stepping time | Reported outcome |
|---|---|---|---|
| Walking disturbance with normal gait planner | 3 N in one horizontal direction and 4 N in another at 2.2 s | Not specified as an anti-push parameter | Recovery after about two cycles, with a shift in walking direction |
| Single-support disturbance without anti-push control | 10 N | Not applicable | Fall during single support |
| Stepping-in-place disturbance without anti-push control | 30 N in one direction and 40 N in another at 2.2 s | Not applicable | Fall under the resultant push |
| Stepping-in-place recovery with anti-push control | 30 N in one direction and 40 N in another at 1.35 s | 0.6 s | Recovery to stepping-in-place state |
| Severe push with anti-push control | 30 N in one direction and 150 N in another at 1.35 s | 0.6 s | Fall because the required capture point is not reachable |
8. Findings and Implications for Humanoid Robot Development
The dissertation reports several findings for the biped humanoid robot. A 20-degree-of-freedom model can produce stable walking when the center of mass and foot trajectories are planned with a linear inverted pendulum model. Decomposing the motion into coronal and sagittal planes simplifies the planning problem while preserving the essential walking behavior. The physical tests on a small humanoid robot show that the planned gait can be executed on real hardware across a hard tabletop, a rubber mat, and a hard carpet. The improved swing foot trajectory reduces landing impact and makes the center of mass height closer to constant.
The anti-push study shows that capture point and orbital energy provide a useful framework for push recovery in a humanoid robot. By detecting an increase in orbital energy and planning a recovery step, the humanoid robot can return to a stable state for moderate pushes. The simulation results demonstrate recovery when the push is within reach and fall when the push exceeds the humanoid robot’s physical limits. The dissertation therefore presents the method as a practical starting point for anti-push control in small biped humanoid robots.
The work also highlights broader implications. A humanoid robot intended for real environments must handle not only level ground but also friction changes and unexpected contact. The combination of a linear inverted pendulum gait planner with a capture-point recovery planner offers a modular structure. The gait planner handles normal walking, while the anti-push planner handles disturbances. This separation can simplify implementation and testing. For small humanoid robots with limited computation, such modularity may be particularly valuable.
9. Limitations and Future Work
The dissertation acknowledges several limitations. The gait algorithm is tested on hard, rubber, and carpet surfaces, but it does not solve walking on highly uneven terrain. The humanoid robot’s ability to adapt to irregular ground remains limited. In the anti-push method, the stepping time is treated as a fixed value, so the humanoid robot does not adjust landing time according to push magnitude. This reduces recovery performance when the push is large. In addition, the method does not compensate for torso inclination after a push, which means a strong push can still cause a fall. The humanoid robot’s maximum step length and joint speed also constrain recovery.
Future work suggested by the dissertation includes adding depth cameras or lidar to the humanoid robot so it can perceive its surroundings and adapt to terrain. Another direction is to improve the anti-push algorithm by computing stepping time from a desired foot placement, rather than fixing it in advance. This could make the humanoid robot more responsive to different push magnitudes. Further work could also incorporate torso inclination control and whole-body motion to expand the range of recoverable disturbances. For the biped humanoid robot, these improvements would move the platform closer to reliable operation in human environments.
10. Conclusion
The master’s engineering dissertation presents a complete study of gait planning and anti-push control for a biped humanoid robot. It builds a 20-degree-of-freedom model, derives forward and inverse kinematics, applies a linear inverted pendulum model in the coronal and sagittal planes, and generates stable walking trajectories for the humanoid robot. Simulation in the Robot Operating System and V-REP validates the gait, while physical tests on a small humanoid robot demonstrate stable walking on multiple surfaces. The swing foot trajectory is refined to reduce landing impact. For anti-push capability, the dissertation uses capture point theory and orbital energy to plan recovery steps. Simulation results show that a stepping-in-place humanoid robot can recover from a moderate push and falls when the push exceeds its physical limits. The work contributes a practical gait planning framework and a simulation-validated anti-push method for the biped humanoid robot, while pointing toward future improvements in terrain awareness, adaptive stepping time, and whole-body recovery control.