Unified Kinematic and Dynamical Modeling of a Soft Robotic Arm by a Piecewise Universal Joint Model

Abstract

The compliance of soft robotic arms renders the development of accurate kinematic & dynamical models especially challenging. The most widely used model in soft robotic kinematics assumes Piecewise Constant Curvature (PCC). However, PCC fails to effectively handle external forces, or even the influence of gravity, since the robot does not deform with a constant curvature under these conditions. In this paper, we establish three-dimensional (3D) modeling of a multi-segment soft robotic arm under the less restrictive assumption that each segment of the arm is deformed on a plane without twisting. We devise a kinematic and dynamical model for the soft arm by deriving equivalence to a serial universal joint robot. Numerous experiments on the real robot platform along with simulations attest to the modeling accuracy of our approach in 3D motion with load. The maximum position/rotation error of the proposed model is verified 6.7x/4.6x lower than the PCC model considering gravity and external forces.

Control of a Soft Robotic Arm Using a Piecewise Universal Joint Model

“…In our previous work [21], we cast an analogy of the motion characteristics of a multi-segment soft arm to a series of rigid link mechanisms, namely, universal joints. We presented a Piecewise Universal Joint model which captures the kinematics and dynamics of a soft robotic arm as a serial interconnection of universal joints (a favorable attribute being that a single universal joint was proven sufficient to model one segment of the robot).…”

“…We presented a Piecewise Universal Joint model which captures the kinematics and dynamics of a soft robotic arm as a serial interconnection of universal joints (a favorable attribute being that a single universal joint was proven sufficient to model one segment of the robot). We proceed to briefly recap the dynamical model developed in [21] for completeness.…”

“…The coordinate system {S i } is obtained from {S i−1 } via four sequential operations in the corresponding coordinate frames: taking the moving frame {S i } and frame {S i−1 } to be initially coincidental, we 1) translate along the z-axis by d i 1 , 2) rotate around the translated y-axis by θ i 1 , 3) rotate around the translated/rotated x-axis by θ i 2 , and finally, 4) translate along the translated and twice rotated z-axis by d i 2 (see Figure 2(b)). The parameters d i 1 , θ i 1 , θ i 2 , and d i 2 represent the configuration variables for the i-th segment and the homogeneous transformation matrix, which transforms vectors from coordinate frame {S i } to coordinate frame {S i−1 }, is given by [21]:…”

“…where c θ , s θ respectively abbreviate cos θ, sin θ. The transformation matrix is usually measured from sensors such as Motion Capture Systems (MCS), and can be used to extract the configuration variables as detailed in [21].…”

“…In effect, the PCC model assumes that each segment of the arm is deformed along a circular arc, which is not realistic in practical 3D applications. In our previous work [21], we proposed a simplified modeling method for soft robot arms which capitalizes on a Piecewise Universal Joint (PUJ) principle: it regards each segment of the soft arm as a universal joint, under the less restrictive assumption that it deforms on a plane without twisting. In brief, we established that the PUJ model describes the soft arm more accurately than the PCC model in the presence of external load.…”