An experimental study on energy-based control of rigid parallel series elastic actuator

SPIRO: A Compliant Spiral Spring–Damper Joint Actuator With Energy-Based Sliding-Mode Controller

“…We now check the stability of the adaptive damper with the given energy-based controller in the proposed Lyapunov function (24). Let's assume the function's energy term is bounded (21) due to the maximum deflection angle q s ∈ [−q s,max , q s,max ] and velocity qs ∈ [− qs,max , qs,max ] and similar properties on the motor states x m ≤ x max ; then, the function candidate V e should be stable around equilibrium {q s,d , qs,d } with satisfying LaSalle's theorem. It can be seen the function in Eq.…”

“…In lower limb locomotion, spring-based compliant joints have been studied for stable trajectories and regenerative energy during motion [7]. However, some of these compensation strategies can over-complicate the issue and result in limited and bulky actuators that are challenging to implement in practice with to design more compact VSAs using vortex forms [20], [21].…”

“…The presence of a spring component (stiffness) in a system can make it unstable, posing a classic problem in control theory [12], [21], [27]- [31]. Optimal controller methods have been applied to efficiently execute compliant actuators by releasing saved energy at the right time considering passivity [12], [27].…”

“…Optimal controller methods have been applied to efficiently execute compliant actuators by releasing saved energy at the right time considering passivity [12], [27]. Robust sliding mode control, proposed by Wang [29], and methods combining energy-based approaches [12], [21], [28] have also been used for complex tasks under disturbance. Spyrakos et al introduced the concept of passivitypreservation control (PPC) to address the challenge of variable impedance control due to induced energy-injecting elements in compliant systems [32].…”

“…In this work, we introduce "SPIRO," a compact compliant actuator capable of dynamically adjusting its impedance in response to external disturbances. We address limitations of prior variable stiffness actuators, which faced challenges like active stabilization issues and lacked easily designable damping profiles, especially for spiral spring models [3], [10], [14], [21]. The proposed mechanism achieves continuous stiffness modulation with precise control at the load-end due to dualmotor integration.…”