Shanghai University Team Boosts Jumping Robot Precision with Pneumatic Elastic Joint and BP-PID Control
In a significant leap for soft robotics and bio-inspired locomotion, engineers at Shanghai University have demonstrated a high-precision control method for a pneumatic series elastic joint—specifically designed for bionic jumping robots—that drastically improves both positional accuracy and variable stiffness tracking. The team, led by Shen Shuang, Lei Jingtao, and Zhang Yuewen, published their findings in China Mechanical Engineering, Vol. 32, No. 12 (June 2021), revealing how a neural-network-tuned PID controller can reduce position tracking error by over 80 percent and stiffness error by more than 80 percent compared to conventional PID control.
The advance matters deeply for engineers building agile, resilient legged robots—particularly those targeting high-dynamic maneuvers such as hopping, landing, and obstacle negotiation in unstructured environments. Unlike rigid serial-link manipulators, jumping robots demand compliant actuation: joints must store and release energy efficiently, absorb shocks without damage, and adapt stiffness rapidly to changing terrain or task requirements. This is where the concept of the series elastic actuator (SEA) becomes essential—and where Shanghai University’s latest contribution stands out.
Traditionally, SEAs use electric motors or hydraulic cylinders paired with mechanical springs to introduce compliance between the motor and the load. While effective, such designs tend to be heavy, bulky, and power-intensive—major constraints for lightweight mobile platforms. The team’s innovation lies in replacing electromechanical or hydraulic drivers with pneumatic artificial muscles (PAMs)—soft, contractile actuators powered by compressed air. PAMs mimic the behavior of biological muscles: they are lightweight, generate high force-to-weight ratios, and inherently exhibit compliance due to air compressibility and elastomeric sheathing.
But pneumatic systems bring their own challenges: strong nonlinearity, hysteresis, time-varying dynamics, and sensitivity to load changes. Controlling them for precise multi-variable tasks—especially simultaneous position and stiffness regulation—has remained a formidable hurdle.
To meet this challenge, the Shanghai team developed a compact, dual-sided joint architecture that isolates the PAM and the series spring on opposite sides of a lever system, connected via low-friction pulleys. This layout decouples actuator deformation from spring elongation geometrically while enabling torque amplification or motion range tuning simply by swapping pulley radii. In their prototype, a 192 mm Festo DMSP-type PAM drives a joint with a 105-degree angular range when paired with a 10 mm radius SEA pulley—far exceeding typical ranges for similarly sized pneumatic joints.
Critically, their mechanical design allows independent modulation of joint stiffness—not through mechanical reconfiguration or antagonistic pairing (which doubles actuator count), but by exploiting the intrinsic relationship between air pressure inside the PAM, the compression of the series spring, and the resulting joint torque gradient. Using the well-established Chou model for PAM force generation—a physics-informed formulation grounded in virtual work and energy conservation—the researchers derived an analytical expression for joint stiffness:
$$k_theta = frac{partialtau}{partialtheta}$$
where $tau$ is the net output torque and $theta$ is the joint angle. Their derivation shows that stiffness scales directly with supply pressure and SEA spring constant—but crucially, not linearly. In fact, simulations reveal a pronounced saturation effect: as the series spring becomes stiffer—say, from 1 kN/m to 100 kN/m—the achievable stiffness range widens (from ~0.07 N·m/rad to ~2.67 N·m/rad under 0.1–0.8 MPa), but the relative modulation bandwidth shrinks. At 1 kN/m, joint stiffness can be tuned over nearly an order of magnitude; at 100 kN/m, tuning is limited to less than a 10x swing. This insight allows designers to select spring stiffness based on mission profile: low-impedance exploration tasks favor softer springs; high-force takeoff or payload lifting favors stiffer ones.
Yet analytical models alone don’t guarantee control performance. Real-world factors—friction in pulleys, dead volume in tubing, sensor noise, and unmodeled air leakage—introduce deviations that standard controllers struggle to correct in real time. Here, the team introduced a BP-PID hybrid control architecture: a three-layer backpropagation neural network (4 inputs, 5 hidden neurons, 3 outputs) continuously tunes the proportional, integral, and derivative gains of a discrete incremental PID controller during operation.
The inputs to the neural network include the reference signal, actual output, tracking error, and a bias term; the outputs are the updated $k_P$, $k_I$, and $k_D$ values. Training occurs online via gradient descent with momentum, ensuring fast convergence without offline data collection. Importantly, the network doesn’t replace the PID—it augments it, preserving the interpretability and robustness of classical control while adding adaptive capability.
In simulation, the BP-PID controller achieved position tracking error of just 0.10 degrees—compared to 0.58 degrees with standard PID—on a 5th-order trajectory (typical of smooth leg swing motions). Stiffness tracking error dropped from 0.026 to 0.005 N·m/rad. Even more revealing: when the SEA spring stiffness was varied (20, 50, and 100 kN/m), the BP-PID controller consistently outperformed PID—and showed lower error with softer springs, confirming that increased mechanical compliance actually aids closed-loop control when paired with an adaptive algorithm.
Experimental validation used a custom test rig featuring a Festo proportional valve (VPPM-6L-L-1-G18), a NI USB-6212 data acquisition system, and dual optical encoders for joint and muscle displacement. The SEA spring was calibrated at 25 kN/m; the return spring at 700 N/m. Position experiments used a scaled trajectory (0–42 degrees) to stay within the 0.1–0.7 MPa safe operating pressure range. Results matched simulation trends: BP-PID reduced average position error from 0.347° to 0.117°, with peak error falling from 1.56° to 0.51°. The response was also noticeably smoother—PID exhibited step-like corrections, while BP-PID tracked with continuous, anticipatory adjustments.
For stiffness experiments, the team commanded a sinusoidal profile (0.7 sin(2πt) + 1.1 N·m/rad), reflecting realistic modulation during stance (high stiffness for push-off) and swing (low stiffness for swing-leg retraction). BP-PID achieved a stable average error of 0.019 N·m/rad versus 0.024 for PID—and cut response time nearly in half (54 ms vs. 124 ms). Though absolute stiffness errors appear small, in hopping dynamics they translate directly into energy loss or instability: a 0.02 N·m/rad deviation at mid-stance can shift peak ground reaction force by several newtons, enough to cause foot slippage or uncontrolled rebound.
From a systems perspective, the Shanghai approach offers three key advantages over prior art. First, hardware simplicity: only one PAM and one series spring are needed per joint—no antagonistic pairs, no dual-valve pressure regulation, no embedded torque sensors. Stiffness emerges from pressure and geometry, not redundant actuators.
Second, energy efficiency: during landing, kinetic energy compresses the SEA spring and retracts the PAM, storing energy elastically. On takeoff, releasing pressurized air adds power to the spring’s recoil—effectively power-modulating the jump, much like the Salto robot from UC Berkeley. Simulations suggest potential energy recovery rates exceeding 40 percent of impact energy, depending on landing velocity and spring preload.
Third, scalability: the pulley-based transmission decouples actuator stroke from joint rotation, enabling compact integration into multi-degree-of-freedom limbs. The team’s 3D-printed prototype weighs under 850 grams—including motor, valve, and structure—making it viable for sub-5 kg hopping platforms.
That said, limitations remain. Air compressibility imposes bandwidth constraints: the tested system achieves ~5 Hz tracking for stiffness and ~8 Hz for position—adequate for hopping (typically 1–3 Hz strides), but insufficient for walking or rapid reflexes. Future work could explore hybrid pressurization (e.g., high-pressure reservoirs for bursts, low-pressure for fine control) or predictive feedforward using learned dynamics.
Equally important is robustness to payload variation. The current model assumes known $m_1$ (link mass) and $m_2$ (foot/load mass), but real robots may grasp objects or wear modular tools. Adaptive identification of inertial parameters—possibly integrated into the BP network’s hidden layer—could address this.
The implications extend beyond robotics. The BP-PID framework is transferable to other nonlinear actuators: shape-memory alloys, dielectric elastomer actuators, or even hydraulic systems with soft seals. In prosthetics, variable-stiffness joints could enable smoother transitions between walking, sitting, and stair-climbing—without requiring user mode selection. In industrial cobots, compliant SEA joints could allow safe physical collaboration while retaining the precision needed for assembly tasks.
From a commercial standpoint, Festo and other pneumatic component suppliers already offer off-the-shelf PAMs and precision valves—reducing barriers to adoption. The control algorithm, implemented in MATLAB/Simulink as an S-function, could be ported to embedded platforms (e.g., dSPACE, Speedgoat, or even ARM Cortex-M7 with floating-point unit) with minimal latency overhead.
Looking ahead, the team’s next steps appear to focus on multi-joint coordination. A single SEA joint is impressive—but hopping requires synchronized action at hip, knee, and possibly ankle. How does stiffness modulation at one joint affect energy flow through the leg? Can centralized BP tuning coordinate multiple valves to minimize total air consumption? These are open questions demanding hardware-in-the-loop validation.
Still, the present work establishes a compelling benchmark: by marrying mechanical compliance with algorithmic adaptability, engineers can overcome longstanding trade-offs between safety, efficiency, and precision. In the race to build robots that move like animals—not just machines—softness is no longer a liability. It’s an asset. And when paired with the right control intelligence, it becomes a superpower.
As legged robotics enters its third decade of modern revival—from Raibert’s hoppers in the 1980s to Boston Dynamics’ Atlas today—the field is shifting from brute-force dynamics to embodied intelligence. The Shanghai University team hasn’t just built a better joint. They’ve shown how structure and control must co-evolve—a principle as true in biology as it is in engineering.
Their approach reflects a growing consensus: the future of mobile manipulation lies not in maximizing rigidity, but in mastering controlled compliance. Whether leaping over rubble in disaster zones or assisting elderly users in homes, tomorrow’s robots will need to be strong and gentle, fast and careful, powerful and perceptive. This work brings that vision one step closer to reality.
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Author: Shen Shuang, Lei Jingtao, Zhang Yuewen
Affiliation: School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China
Journal: China Mechanical Engineering, Vol. 32, No. 12, pp. 1486–1493 (June 2021)
DOI: 10.3969/j.issn.1004-132X.2021.12.013