Hybrid Position‐Compliance Control of Redundantly Actuated Parallel Kinematic Manipulators Equipped with Serial Elastic Actuators

Abstract

Redundantly actuated parallel kinematic manipulators (RA‐PKM) are ideal candidates in robotic applications combining dynamic performance with high accuracy. Actuation redundancy further allows for modulation of the end‐effector (EE) stiffness. A recent trend in robotics is the use of inherently compliant and elastic components, eventually leading to soft continuum robots, which shall provide tailored solutions for human‐robot collaboration and assistance applications. One way to introduce compliance is to use serial elastic actuators (SEA). This yields two kinematically decoupled dynamic systems, the RA‐PKM mechanism and the actuation system, that are force‐coupled by (passive) elastic elements. The DOF of the actuation system exceeds the DOF of the RA‐PKM according to the degree of actuation redundancy. Due to the kinematic decoupling the RA‐PKM is underactuated. To address this issue, a flatness‐based feedback‐linearizing position control approach along with a stiffness modulation approach is proposed.

Time‐optimal trajectory planning of a redundantly actuated planar parallel robot driven with series elastic actuators

“…Various approaches for the dynamic modeling of PKM equipped with rigid actuators are established in [6][7][8][9]. For PKM equipped with SEA the derivation of the equations of motions (EOM) can be found in [10]. In the following Sections 2.1 and 2.2 only the final motion equations are provided to highlight the systems' properties addressed in Section 3.…”

“…𝐱 min ≤ 𝐱 ≤ 𝐱 max , ⃛ 𝐳 min ≤ 𝐯 ≤ ⃛ 𝐳 max , 𝐮 min ≤ 𝐮 ≤ 𝐮 max (10) with the time weight 𝑤 𝑡 , the actuation weight 𝑤 𝑢 and the initial 𝐱 𝑇 0 = [𝐳 𝑇 0 , 𝟎 𝑇 , 𝟎 𝑇 ] and terminal states 𝐱 𝑇 𝐸 = [𝐳 𝑇 𝐸 , 𝟎 𝑇 , 𝟎 𝑇 ]. Conditions ( 9) and (10) form the box constraints for all joints, the EE-trajectory and all actuation torques, respectively.…”

“…The anticipated bang-bang behaviour of the motor torques is clearly visible and it can be seen, that similar results are achieved both, for the redundantly and non-redundantly actuated PKM. All moments of inertia and masses of the PKM can be found in [10]. For actuation torque limits 𝑢 𝑖,min = −0.3 Nm and 𝑢 𝑖,max = 0.3 Nm each and for all spring stiffnesses 𝑐 𝑖 = 1 Nm∕rad are chosen.…”