A series elastic actuator has a single torque port and pays for it twice: the geared motor must swing its own reflected inertia through the spring, so the amplitude it delivers collapses as ω−2 in the command frequency ω once it saturates, while commands below the transmission's breakaway friction never arrive at all. This letter opens a second torque port on the load side, placing a frameless direct-drive micro motor in parallel with a fixed-stiffness spring -- a parallel-integrated SEA, or Pi-SEA, whose delivered torque is read from spring deflection and micro current without a sensor -- and dividing the commanded torque between the two channels by time scale rather than by filter design. The micro torque loop is the fast subsystem, which makes the closed loop singularly perturbed and turns the separation the channels need into a bound to check rather than a crossover to tune; a leaky mid-ranging integrator returns the steady load to the spring; and the amplitude ceiling, read backwards, becomes a closed-form sizing rule that matches spring, geared motor and micro motor to the amplitudes and frequencies an application asks for. Against SEAs, the Pi-SEA widens the tracked band at small amplitudes and lowers the residual the joint imposes on its environment, each by an order of magnitude.
Figures & tables
Fig. 1: Single-joint model of the parallel-integrated SEA. The slow subsystem is the compliant SEA–load interaction, the fast subsystem the torque loop of the load-side micro motor, whose torque reaches the load without passing through the spring or the reduction.
Fig. 2: Dual-time-scale allocation: the macro channel is force-controlled on the spring deflection with a leaky mid-ranging integral, the micro channel renders the residual τd−Fs , and both act on the common load.
Fig. 3: The sizing rule ( 16 ) as a design surface for the 10 N m at 20 Hz specification. Height and colour are the micro torque Tμ the rule requires at each (Ks,τmmax/Jm) , falling to zero where the macro channel already covers the specification alone; a motor serves everything below its own magenta iso-line. The orange curves section the surface at the as-built joint; the shortfall they show is a prediction at the joint’s peak torque, quantified in the text.
Fig. 4: The prototype as built. (a) Cross-section: the torsion spring ( Ks ) and the frameless micro motor ( τμ ) act in parallel on the load, and an absolute encoder across the spring measures θs . (b) The assembled joint and its bench. One EtherCAT master closes both loops at 1000 Hz over three slaves; the spring doubles as the torque sensor, so no external transducer is in the loop.
Symbol
Value
Symbol
Value
Jm [kg m 2 ]
1.56
Kps [N m/rad]
8000
Bm [N m s/rad]
12.2
Kds [N m s/rad]
160
τb [N m]
9.0
KI , λ [1/s]
10, 0.1
Ks [N m/rad]
780
Nd , ωQ [rad/s]
300, 50
kt (meas.) [N m/A]
0.105
Jl bar / link [kg m 2 ]
0.071 / 0.30
ωμ/2π [Hz]
745
aμ [rad/s]
112
TABLE I: Parameters identified on the assembled prototype and the gains and load conditions used.
Fig. 5: Closed-loop Tid/τd , load clamped, identical gains. (a) 0.5 N m and (b) 2 N m chirps, 0.3–20 Hz, drawn where the coherence exceeds 0.5; (a) adds the fixed command split at 2 and 18.1 Hz, (b) the Pi-SEA split into Fs and τμ , with τμ under the frictionless model dashed and both −3 dB points dotted—the gap is the allocation responding to delivered torque, which no fixed filter of τd does. (c) 5 N m, with the splits at 10 Hz, and (d) 15 N m stepped sines; hollow markers were cut short by the spring-energy guard.
Fig. 6: Where each controller tracks the command ( ∣1−Tid/τd∣≤0.5 ) with the load clamped, under the τmmax=100 N m software clamp of this campaign, not the joint’s 170 N m peak. Orange, the region the macro-only loop already tracks; blue, the band the micro motor adds; white, neither. Markers are the four measured amplitudes, the 0.5 N m Pi-SEA edge from stepped sines past the chirp; the boundaries between them are interpolated. Dotted, the macro amplitude ceiling τmmaxKs/(Jmω2) of ( 16 ); dashed, that ceiling plus Tμ ; dash–dot, the spring-energy guard of the test rig, which is what stops the 15 N m row at 7 Hz.
Fig. 7: Leaky mid-ranging, load clamped. (a) 1 N m step with KI=10 : the micro motor carries the edge and the spring channel takes the load over. (b) Micro torque after the same step with the DOB off for λ=0.1,0.2,0.5 s -1 (purple) and with the DOB on for λ=0.1 (grey).
Fig. 8: Free symmetric bar ( Jl=0.071 kg m 2 ). (a) Closed-loop gain ∣Tid/τd∣ of the 2 N m chirp with ( 5 ) (dark) and with τff=τd (light); dotted, the low-frequency share of the latter. (b), (c) Residual output torque under τd=0 while the bar is pushed by hand, slow and fast, against the bar rate: raw samples faint, fitted loops dark (median torque in equal-count rate bins on each branch of the stroke).
Fig. 9: Torque tracking on the gravity link (bar with 2.5 kg at 0.3 m, hanging start): (a) sine 1 N m at 0.3 Hz, (b) triangle ±5 N m at 0.25 Hz, (c) sine 12 N m at 4 Hz with ( 5 ). Rows: command and delivered torque; error τd−Tid (raw faint, filtered dark); Pi-SEA split into Fs and τμ . One run of each controller is shown.
Designing robots for high-torque, high-fidelity haptic interaction is challenging. Parallel Elastic Actuators (PEAs) use elastic elements in parallel to smaller motors to complement torques, and Series Elastic Actuators (SEAs) use elastic elements in series to decouple motor impedance and improve force control. Recent work combines SEAs and PEAs to obtain both benefits but requires separate elastic elements or clutching. This paper presents the Series Parallel Integrated Nonlinear Elastic Actuator (SPINEA), which merges SEA and PEA such that a single elastic element takes on dual roles simultaneously, parallel and series. This is achieved by a nonlinear transmission in which the motor and load have misaligned rotation axes and are elastically connected. This geometry enables both high peak torque and precise torque tracking. We apply SPINEA to actuate lean of a haptic bicycle simulator, which requires high moments and precise rendering for safe and realistic rider interactions. We realized a prototype and performed experiments, both with an external excitation setup and with riders cycling. Our results confirm SPINEA's low impedance and precise torque tracking, up to 4.25 Hz with the bicycle frame fixed and up to 4 Hz with riders. The benefits may transfer to other applications requiring compact, high-performance actuation.
Christina Kohler, Michiel Plooij, Nuria Peña-Perez +2
Institute of Automatic Control, RWTH Aachen University, 52074 Aachen, Germany · Demcon Life Sciences & Health, 2628 Delft, The Netherlands · Hapticlink Technologies, 2611 Delft, The Netherlands +2
Series and parallel elastic actuators offer complementary but mutually exclusive advantages, yet no existing actuator enables real-time transition between these topologies during operation. This paper presents a novel actuator design called the Dual-Topology Elastic Actuator (DTEA), which enables dynamic switching between SEA and PEA topologies during operation. A proof-of-concept prototype of the DTEA is developed to demonstrate the feasibility of the topology-switching mechanism. Experiments are conducted to evaluate the robustness and timing of the switching mechanism under operational conditions. The actuator successfully performed 324 topology-switching cycles under load without damage, demonstrating the robustness of the mechanism. The measured switching time between SEA and PEA modes is under 33.33 ms. Additional experiments are conducted to characterize the static stiffness and disturbance rejection performance in both SEA and PEA modes. Static stiffness tests show that the PEA mode is 1.53x stiffer than the SEA mode, with KSEA = 5.57 +/- 0.02 Nm/rad and KPEA = 8.54 +/- 0.02 Nm/rad. Disturbance rejection experiments show that the mean peak deflection in SEA mode is 2.26x larger than in PEA mode (5.2 deg vs. 2.3 deg), while the mean settling time is 3.45x longer (1380 ms vs. 400 ms). The observed behaviors are consistent with the known characteristics of conventional SEA and PEA actuators, validating the functionality of both modes in the DTEA actuator.
Vishal Ramesh, Aman Singh, Shishir Kolathaya
Department of Cyber-Physical Systems (CPS), Indian Institute of Science (IISc), Bengaluru, India
In robotic applications, actuators are typically designed to be stiff with minimal backlash to ensure precision and repeatability. However, this limits compliance, leading to potential damage and poor force control in uncertain environments. Series Elastic Actuation (SEA) introduces compliance to enhance disturbance rejection and enable force measurement via Hooke's Law but reduces system bandwidth. A custom Series Elastic (SE) element was retrofitted to a black-box actuator to mitigate non-linearities like backlash and static friction. Integrating the SE element enabled high-fidelity force measurements, improving force control bandwidth and performance. A torsional SE element was designed through Finite Element (FE) analysis, yielding a stiffness of 2155.4 Nm/rad. Open-loop force control bandwidth was measured for the original motor and the SEA-integrated configuration, while closed-loop bandwidth was assessed using feedback from the SEA and a commercial force sensor. The SEA module increased bandwidth from 10.32 Hz to 30.32 Hz, a 2.93X improvement. Additionally, it outperformed the commercial sensor by 7.63% despite costing 25 GBP, a fraction of the price.
Ivan Tregear, Ayhan Aktas, Ferdinando Rodriguez y Baena
Imperial College London, Mechanical Engineering Department, UK · KAIKAKU.AI, London, N1 6NG, UK · Imperial College London, Mechanical Engineering Department, SW7 2AZ, UK