Humanoid robots have long been envisioned as assistants or replacements for humans in diverse scenarios such as factories, households, disaster rescue, and anti-terrorism operations. The realization of this vision hinges on the robots’ motion performance, which, despite significant advancements, has not yet fully matched human capabilities. A critical factor influencing this performance is the leg configuration of the humanoid robot, which fundamentally determines dynamic balance, load capacity, and energy efficiency. This article delves into the historical evolution, current state, and future prospects of leg configurations in humanoid robots, emphasizing the structural paradigms that underpin their locomotion.
The study of humanoid robot legs draws inspiration from human biomechanics. The human lower limb comprises the hip, knee, and ankle joints, simplified as kinematic pairs: the hip as a spherical joint (RRR), the knee as a revolute joint (R), and the ankle as a universal joint (RR). This anatomical basis informs the typical design of humanoid robot legs with six degrees of freedom (DOF): three at the hip (pitch, roll, and yaw), one at the knee (pitch), and two at the ankle (pitch and roll). Furthermore, the Hill muscle model, which includes contractile, series elastic, and parallel elastic elements, inspires the development of actuators for humanoid robots, leading to variants like Series Elastic Actuators (SEA) and Quasi-Direct Drive actuators (QDD).
The historical trajectory of humanoid robot leg configurations is marked by pivotal developments. In 1969, the Waseda University team introduced the WL-3 robot, employing electro-hydraulic servo drives and master-slave control, marking the inception of humanoid robotics. A significant shift occurred in 1983 with the WR-10R robot, which utilized rotary actuators directly placed at joint positions, establishing the serial configuration as a standard. The landscape evolved in 2006 when the LOLA robot from the Technical University of Munich incorporated a parallel linkage mechanism in the ankle, pioneering the hybrid serial-parallel leg configuration. Subsequent innovations, such as the THOR robot from Virginia Tech in 2014, which used linear actuators throughout the leg, and the YC robot from UBTECH in 2021, featuring a hybrid configuration with QDD actuators for torque control, underscore the continuous refinement in this domain.
Serial configurations, characterized by a chain of links connected by joints, are prevalent due to their simplicity and large workspace. In its basic form, all actuators are co-axial with their respective joints. However, this leads to high joint inertia and suboptimal mass distribution, impairing dynamic performance. To mitigate these issues, some designs relocate certain actuators away from the joint axes, using linkages or belt drives for motion transmission. For instance, in the HUBO series, the hip pitch actuator’s motor is positioned at the mid-thigh, connected via a synchronous belt to the reducer at the hip joint. Similarly, the TORO robot places the ankle pitch actuator at the shank center, employing a linkage to transmit motion to the ankle joint. The HRP-4 robot further exemplifies this approach by situating ankle actuators proximally to reduce leg inertia. Despite these improvements, serial configurations inherently suffer from lower stiffness due to the extended transmission chain, limiting their load capacity and dynamic response. The dynamics of a humanoid robot can be approximated using an inverted pendulum model. For a 3D linear inverted pendulum, the motion is governed by:
$$ \ddot{x} = \frac{g}{h} x $$
where $x$ is the horizontal position of the center of mass (CoM), $g$ is gravity, and $h$ is the constant height of the CoM. This model highlights that stability in walking is influenced by the CoM height; higher CoM improves stability. Serial configurations often result in a lower CoM and higher leg inertia, constraining performance.
Hybrid serial-parallel configurations merge the advantages of both serial and parallel structures, offering enhanced stiffness, reduced inertia, and higher payload capacity. These configurations often employ parallel mechanisms at the ankle or across multiple joints. For example, the Valkyrie robot from NASA uses a parallel ankle mechanism with linear actuators, sliders, and load cells. The CogIMon robot implements a parallel ankle where actuators near the knee drive the ankle via belts and linkages. The DURUS robot features a compact parallel ankle with linear springs for energy storage and release, achieving low energy consumption. Parallel mechanisms at the ankle, such as the 2-SPU+1U or 2-PUS+1U architectures, provide two DOF while concentrating mass proximally.
Expanding parallel mechanisms to multiple joints further optimizes performance. The WALK-MAN robot positions the knee actuator near the hip, using a linkage to drive the knee joint, and the ankle pitch actuator at the knee, connected via a four-bar linkage. The ASIMO robot relocates ankle actuators to the knee and knee actuators to the mid-thigh, significantly reducing leg inertia. The Digit robot employs a spatial four-bar linkage at the ankle and a compliant thigh structure for safe interaction. Disney’s biped robot concentrates five of its six actuators at the hip, using linkages to achieve full leg mobility. The LEO robot places all three leg actuators at the hip, driving a parallel mechanism for walking, with lightweight materials minimizing inertia. The OmniLeg robot, inspired by human anatomy, uses three hip-mounted actuators and a spatial linkage for omnidirectional motion with low inertia. MIT’s humanoid robot utilizes a hybrid configuration with QDD actuators and belt drives for motion transmission. Our own development, the YC humanoid robot, implements a novel hybrid configuration: the knee actuator is located at the hip, transmitting motion through a simplified five-bar linkage, and the ankle actuator is at the knee, connected via a spatial four-bar linkage. This design markedly reduces hip and knee inertia and raises the CoM, enabling stable walking at 0.4 m/s.
Linear actuators are also employed in hybrid configurations. The LOLA robot uses a linear actuator for the knee, mounted on the thigh, and ankle actuators at the lower hip. The THOR robot employs linear SEAs for all leg joints, with the hip pitch actuator on the thigh and hip roll/yaw actuators at the upper thigh. The RH5 robot features parallel mechanisms in both the thigh and shank. The BHR-T robot uses linear actuators driven by ball screws for the knee and ankle, optimized for running at 7 m/s. Tesla’s Optimus robot proposes a leg with linear actuators for the knee and hip pitch, and a 2-SPRR+1U parallel ankle. The JEG robot incorporates a fiber jamming structure and servos for compliant locomotion.
The performance of different leg configurations can be compared based on rigidity, mass distribution, inertia, and kinematic complexity. Serial configurations offer simplicity in kinematics but lower rigidity and higher inertia. Parallel configurations provide high rigidity and low inertia but have limited workspace and complex kinematics. Hybrid configurations balance these attributes, achieving good rigidity, low inertia, and higher CoM, albeit with increased kinematic complexity. The following table summarizes the comparison:
| Configuration Type | Rigidity | Mass Distribution | Inertia | Kinematics Solving |
|---|---|---|---|---|
| Serial | Poor | Low CoM | High at knee and hip | Simple |
| Parallel | Good | High CoM | Low at hip and knee | Complex |
| Hybrid Serial-Parallel | Good | High CoM | Low at hip and knee | Complex |
The application of parallel mechanisms in notable humanoid robots over time shows a trend towards increased use of parallel DOF across hip, knee, and ankle joints. The table below lists exemplary robots and their use of parallel DOF in leg configurations:
| Humanoid Robot (Year) | Parallel DOF at Hip | Parallel DOF at Knee | Parallel DOF at Ankle | Total Parallel DOF in Leg |
|---|---|---|---|---|
| LOLA (2006) | 0 | 1 | 2 | 3 |
| Valkyrie (2013) | 0 | 0 | 2 | 2 |
| TORO (2014) | 0 | 0 | 2 | 2 |
| THOR (2014) | 3 | 1 | 2 | 6 |
| TALOS (2017) | 0 | 0 | 2 | 2 |
| RH5 (2017) | 1 | 1 | 2 | 4 |
| Disney Biped (2018) | 3 | 1 | 1 | 5 |
| YC (2021) | 1 | 1 | 2 | 4 |
| MIT Humanoid (2021) | 1 | 1 | 2 | 4 |
| Optimus (2022) | 2 | 1 | 2 | 5 |
| BHR-T (2023) | 0 | 1 | 2 | 3 |
Various parallel mechanisms are suitable for different parts of the humanoid robot leg. For the hip, architectures like 3-UPU, 3-PSP, 3-RRR, and 3-R[2-SS] can be used. The knee can employ 1-RRRR or 1-RRPR mechanisms. The ankle may utilize 2-SPU+1U, 2-PUS+1U, 2-SPRR+1U, or 2-SU[1-RRPR]+1U. Combinations of these mechanisms yield numerous possible leg configurations, requiring holistic optimization based on actuators, control models, and application contexts.
Technical challenges in leg configuration design primarily involve the alignment between the mechanical structure and the control model. If the leg configuration does not match the simplified dynamics model used for control, such as the inverted pendulum, the robot must compensate for discrepancies, potentially limiting performance. For instance, the dynamics of a humanoid robot can be expressed using the Euler-Lagrange equations:
$$ \mathbf{M}(\mathbf{q}) \ddot{\mathbf{q}} + \mathbf{C}(\mathbf{q}, \dot{\mathbf{q}}) \dot{\mathbf{q}} + \mathbf{G}(\mathbf{q}) = \boldsymbol{\tau} $$
where $\mathbf{M}$ is the mass matrix, $\mathbf{C}$ represents Coriolis and centrifugal forces, $\mathbf{G}$ is the gravity vector, $\mathbf{q}$ are the joint angles, and $\boldsymbol{\tau}$ are the joint torques. Implementing control strategies like zero-moment point (ZMP) based walking or force control requires accurate dynamic models tailored to the specific leg configuration. The development of actuators also poses challenges; current electric actuators, including SEAs and QDDs, still fall short of the performance of human muscles in terms of power density and efficiency. QDD actuators, which allow torque control via motor current feedback, are gaining traction due to their cost-effectiveness and safety in human-robot interaction.
Recent research hotspots include the extensive exploration of hybrid serial-parallel configurations, particularly for the knee and ankle joints. The adoption of QDD actuators enables direct torque control, facilitating more dynamic and compliant motions. Additionally, the integration of AI techniques, such as deep learning, reinforcement learning, and large language models, is reducing the complexity of kinematic solving and control model development. For example, reinforcement learning can optimize walking gaits directly from experience, bypassing intricate model-based design. The cost function in reinforcement learning for locomotion might be formulated as:
$$ J(\pi) = \mathbb{E}_{\tau \sim \pi} \left[ \sum_{t=0}^{T} \gamma^t r(\mathbf{s}_t, \mathbf{a}_t) \right] $$
where $\pi$ is the policy, $\tau$ is the trajectory, $\gamma$ is the discount factor, and $r$ is the reward function based on state $\mathbf{s}_t$ and action $\mathbf{a}_t$. This approach allows humanoid robots to learn robust and adaptive locomotion strategies.
Looking ahead, several trends are shaping the future of humanoid robot leg configurations. First, there is a clear shift from purely serial designs to hybrid and parallel configurations to achieve higher stiffness, lower inertia, and better dynamic performance. Second, actuators are evolving from rigid types to elastic and quasi-direct drive variants, enabling improved force control and energy efficiency. Third, the use of linear actuators alongside rotary ones is increasing, offering compact design and direct force application. Fourth, control paradigms are moving from position-based to torque-based and hybrid force-position control, allowing more natural and adaptive interactions with the environment. Finally, the co-optimization of actuators, leg configurations, and structural components using advanced materials and AI-driven design is emerging as a key research direction to enhance overall performance.
In conclusion, the evolution of leg configurations in humanoid robots has progressed significantly over the past five decades, from initial serial designs to sophisticated hybrid serial-parallel systems. The imperative for high dynamic performance, guided by principles such as the inverted pendulum model, drives the adoption of configurations that maximize CoM height and minimize leg inertia. Actuator technology and control strategies are intimately linked with leg configuration development, with recent advances in torque control and AI promising further breakthroughs. As research continues, the synergy between mechanical design and intelligent control will undoubtedly lead to humanoid robots with locomotion capabilities approaching or even surpassing those of humans, unlocking their potential in a myriad of real-world applications.