Traditional single-loop control schemes, due to insufficient consideration of the strong coupling and nonlinear friction characteristics of the hip joint, are prone to problems such as large trajectory tracking errors and excessive energy consumption in high-speed motion or complex terrain. In recent years, technological breakthroughs based on the "dual-loop control" architecture and friction compensation feedforward-feedback coordinated strategy have provided a new path for optimizing hip joint performance.
Dual-loop control architecture, decoupling the collaborative optimization of motion and force control
Dual-loop control achieves coordinated control of hip joint kinematics and dynamics through independent optimization and dynamic coupling of the inner loop (force/torque loop) and the outer loop (position loop). Taking model predictive control (MPC) as an example, the inner loop optimizes the control input for the next N time steps in a rolling manner, simultaneously satisfying joint torque, velocity, and position constraints. Laboratory test data shows that after adopting the MPC inner loop, the torque tracking error of the hip joint during squatting movements decreased from ±8% to ±2%, and the response time was shortened to 15 milliseconds, a three-fold improvement over traditional PID control.
The outer-loop position control achieves acceleration continuity through cubic polynomial trajectory planning. For example, during the transition from standing to stepping, the outer-loop controller decomposes the target position into three stages: acceleration, constant speed, and deceleration, and generates a smooth trajectory using Bézier curves. Product testing by a certain company shows that this strategy reduces the hip joint angle tracking error from ±1.2° to ±0.3°, and no overshoot occurs at an angular velocity of 10°/s.
The dual-loop coordination mechanism is achieved through real-time data interaction: the outer loop converts position errors into torque reference values, while the inner loop combines friction compensation feedforward terms to generate the final control command. Taking the Tesla Optimus Gen-2 as an example, its hip joint adopts a three-axis layout of "Yaw-Roll coaxial + Pitch 30° angled," which is achieved through dual-loop control.
Static power consumption: The self-locking roller screw ensures that the joint power consumption is less than 100W when the screw is in a standing position;
Dynamic bandwidth: Small signal response frequency up to 15Hz, supporting heavy-duty actions such as squatting and carrying;
Range of motion: Pitch axis travel from -45° to +120°, covering 90% of the range of motion of the human hip joint.
Friction compensation feedforward-feedback coordination solves the problem of nonlinear interference.
Hip joint friction is a core source of interference affecting control accuracy. Experiments show that the frictional torque of a certain type of harmonic reducer can reach 15% of its rated torque in the low-speed range (<0.1 rad/s), leading to a 40% increase in trajectory tracking error. Traditional feedback control (such as PID) relies on error-driven mechanisms and is prone to oscillation or overshoot during sudden friction changes. The feedforward-feedback collaborative strategy achieves precise friction compensation through a two-layer mechanism of "model prediction + real-time correction".
1. Feedforward layer: Dynamic compensation based on the Stribeck model
The Stribeck model describes frictional characteristics through a combination of static friction, Coulomb friction, and viscous friction, and its formula is:
Ff = Fc⋅sgn(q˙) + (Fs−Fc)⋅e−(q˙/q˙s)2 + σ⋅q˙, where Fs is the static friction force, Fc is the Coulomb friction force, σ is the viscous friction coefficient, and q˙s is the Stribeck velocity. Through genetic algorithm identification of model parameters, testing on a six-axis industrial robot shows that Stribeck feedforward compensation can reduce the position tracking error from ±0.5° to ±0.1°, with no overshoot during sudden velocity changes.
2. Feedback Layer: Real-time Correction of Adaptive Robust Control (ARC)
To address model errors and external disturbances, ARC achieves dynamic compensation by estimating the friction coefficient online and adjusting the control gain. For example, a research team introduced an ARC feedback loop in a hip joint experiment, with the following control law:
τ = M^(q)q¨ + C^(q,q˙)q˙ + G^(q) + Kss + Kds˙, where s is the sliding surface, and Ks and Kd are adaptive gains. Test data shows that ARC reduces the friction compensation error of the hip joint from ±12% to ±3% in the speed range of 0.1-5 rad/s, and the response time to sudden load changes (such as a sudden increase of 5 kg load) is <50 milliseconds.
Technological Breakthroughs from Laboratory to Industrialization
1. Hardware selection and structural optimization
Taking Unitree Robotics' Unitree G1 as an example, its hip joint uses a "three-rotational harmonic reducer" solution:
Yaw axis: Harmonic reducer + 30 N·m torque output, supports trunk balance;
Roll shaft: Harmonic reducer with ±30° travel, suitable for slope travel;
Pitch axis: Coaxial harmonic ±77° travel, covering movements such as climbing stairs.
The design reduces the complexity of the Jacobian matrix by using "approximately concurrent axes", which reduces the inverse solution calculation time from 8 milliseconds to 2 milliseconds. At the same time, it reduces the hip width to 200mm by using a slanted lead screw, which improves the passage of narrow passages.
2. Algorithm Implementation and Performance Verification
In a logistics robot project, a dual-loop control system for the hip joint combined with a friction compensation strategy was implemented.
Energy efficiency optimization: The self-locking lead screw reduces static power consumption from 180W to <5W, extending battery life to 8 hours on a single charge;
Track accuracy: During high-speed walking at 2m/s, the hip joint angle tracking RMS error is <0.5°, and the ZMP stability margin is >5cm;
Impact resistance: Through mechanical self-locking and software torque limiting, the joint damage rate of the robot is reduced by 90% when it falls from a height of 1m.
With the development of AI technology, dual-loop control and friction compensation strategies are being deeply integrated with deep learning. For example, one team proposed a dynamic friction model based on LSTM, which reduces the amount of training data by 90% through transfer learning while improving prediction accuracy by 15%. In addition, the requirements of the ISO 10218 standard for robot safety are driving hip joint design towards "redundant sensing + fault prediction".
From laboratory prototypes to industrial applications, the "dual-loop control" and friction compensation feedforward-feedback collaborative strategy for the hip joint of humanoid robots have become core technologies for overcoming bottlenecks in motion accuracy and energy efficiency. Through hardware selection optimization, algorithm innovation, and engineering practice verification, this technology system is laying the foundation for the widespread application of humanoid robots in fields such as industrial manufacturing, logistics warehousing, and medical care.
