Reconciling distributed compliance with high-performance control in continuum soft robotics

Abstract

High-performance closed-loop control of truly soft continuum manipulators has remained elusive. Experimental demonstrations have largely relied on sufficiently stiff, piecewise architectures in which each actuated segment behaves as a distributed yet effectively rigid element, while deformation modes beyond simple bending are suppressed. This strategy simplifies modeling and control, but sidesteps the intrinsic complexity of a fully compliant body and makes the system behave as a serial kinematic chain, much like a conventional articulated robot. An implicit conclusion has consequently emerged within the community: distributed softness and dynamic precision are incompatible. Here we show this trade-off is not fundamental. We present a highly compliant, fully continuum robotic arm - without hardware discretization or stiffness-based mode suppression - that achieves fast, precise task-space convergence under dynamic conditions. The platform integrates direct-drive actuation, a tendon routing scheme enabling coupled bending and twisting, and a structured nonlinear control architecture grounded in reduced-order strain modeling of underactuated systems. Modeling, actuation, and control are co-designed to preserve essential mechanical complexity while enabling high-bandwidth loop closure. Experiments demonstrate accurate, repeatable execution of dynamic Cartesian tasks, including fast positioning and interaction. The proposed system achieves the fastest reported task-execution speed among soft robots. At millimetric precision, execution speed increases nearly fourfold compared with prior approaches, while operating on a fully compliant continuum body. These results show that distributed compliance and high-performance dynamic control can coexist, opening a path toward truly soft manipulators approaching the operational capabilities of rigid robots without sacrificing morphological richness.

Figures (6)

• Figure 1: From Cobots to Soft Robots. Comparison of physical characteristics across collaborative rigid robots, segmented soft robots, and general soft robots. The table highlights key differences in structure, material softness, actuation, and motion capabilities.
• Figure 2: Experimental Setup and Control Framework. (A) Experimental setup. (B) Internal view of the soft arm. Different tendon configurations are visually distinguished by straight (green) and crossed (blue) paths, while burgundy circles denote the tiny guiding rings. Transparent renderings on the sides illustrate examples of achievable shapes. (C) Top view of the robot illustrating the tendons' placement at the base. Each tendon–motor pair is identified by a number from 1 to 4, with green circles denoting straight tendon paths and blue crosses denoting the crossed ones. (D) Soft robot's workspace attained through combined actuation of the four tendons with pulling forces in $\left[0,-5\right]$ N. (E) Block diagram of the two-level control framework employed, with the inner loop in gray and the outer loop in red.
• Figure 3: Two-dimensional coiling task. (A) (Top) The robot’s final configurations at each reference Cartesian coordinate pair are shown. Reference points are marked with red circles, while the corresponding 3D projections reached by the robot are highlighted with red stars. From right to left, the shapes correspond to time windows of $15$ s, $5$ s and $1$ s, respectively, with a transparency gradient representing progression over time. (Bottom) The projection of the robot’s motion onto the Cartesian plane is shown for each task and time interval. Red circles denote desired target coordinates, while black crosses indicate the robot’s final position before reference change. Motion is reported on a normalized time scale. (B) Time evolution of the errors in operational space and their convergence within $5$ mm and $10$ mm bands. To improve readability, the post-processed error obtained through a moving-average filter is highlighted, while the raw error signal is displayed more transparently in the background. Grey dashed vertical bars indicate the switch in time windows. (C) Time evolution of the estimated actuation coordinates (blue) and their tracking of the reference signals (red) under configuration-space collocated control.
• Figure 4: Four-dimensional triangular shape task. (A) (Top) The robot’s final configurations upon converging at reference points (red circles) displaced in a triangular shape in the Cartesian space are shown. From right to left, the shapes correspond to time windows of $25$ s, $5$ s and $1$ s, respectively. (Bottom) The reconstructed robot’s motion in the Cartesian space is shown for each time interval. The red circle denotes the desired targets, while the black cross indicates the robot's last position before the reference change. Motion is reported on a normalized time scale. (B) Time evolution of the errors in operational space and their convergence within the $5$ mm and $10$ mm accuracy bands. To improve readability, the post-processed error obtained through a moving-average filter is highlighted, while the raw error signal is displayed more transparently in the background. Grey dashed vertical bars indicate the switch in time windows. (C) Time evolution of the pulling forces exerted by the tendons. (D) Time evolution of the estimated actuation coordinates (blue) and their tracking of the reference signals (red) under configuration-space collocated control.
• Figure 5: Pendulum-like ball striking. (A) The time sequence of shapes attained by the soft manipulator is reported here. The ball is first released at $t=0.00$ s, and then accurately struck at $t=0.35$ s by the robot. (B) The motion of the robot tip together with the trajectory of the marker placed on the external surface of the pendulum is shown. The corresponding normalized time histories are reported on the left (soft robot) and on the right (pendulum). The trajectories include cross markers, shown in the corresponding colors, to identify the impact instant; post-impact trajectories are subsequently displayed with increased transparency. In addition, the desired target position for the robot's tip is indicated by the gray circle, while the nominal trajectory of the pendulum's marker in the absence of impact is depicted by the black dashed line.