Safe Supervisory Control of Soft Robot Actuators
Andrew P. Sabelhaus, Zach J. Patterson, Anthony T. Wertz, Carmel Majidi

Abstract—Although soft robots are claimed to show safer
interactions with their environment than traditional robots,
soft mechanisms and actuators still have significant potential
for damage or degradation. This article introduces a feedback
strategy for safe soft actuator operation during control of asoft robot during unmodeled environmental contact. To do so, asupervisory controller monitors actuator state and dynamicallysaturates control inputs to avoid conditions that could lead tophysical damage. We prove that, under certain conditions, thesupervisory controller is stable and verifiably safe. We thendemonstrate completely onboard operation of the supervisory
controller using a soft thermally-actuated robot limb with embedded shape memory alloy (SMA) actuators and sensing. We
present experiments which show that our approach prevents
overheating during contact (including environmental constraints
and human contact) or when infeasible motions are commandedfrom learning from demonstration. This supervisory controller,and its ability to be executed with completely onboard sensing,has the potential to make soft robots reliable enough for practicaluse.

Fig. 1: Operation of the safe supervisory control scheme on athermally-actuated shape memory alloy (SMA) soft robot limb
during human contact (a) prevents overheating (b). Results
using onboard temperature and position sensors verify safe
temperatures (c), in blue, versus unsafe control, in red.

I. I NTRODUCTION
One of the most prevalent claims about soft robots istheir intrinsic safety when interacting with humans or theenvironment (Laschi et al. [4], Majidi [5]). Less commonly
discussed are new challenges in safety introduced through theuse of novel soft actuators required for generating roboticmotion. Soft actuators can fail dramatically, as practitioners
may recognize. Informally, pneumatic balloons can pop, thermal actuators can overheat and cause fire risks (Soother et al.
[8]), and dielectrics can cause dangerous arcing (Bilodeau andKramer [1]), among others. As of yet, these risks have been
mitigated by simple bespoke system designs, hard limits on
actuation input (Yee Harn Teh and Featherstone [10]), or openloop actuation (Patterson et al. [6]). Incorporating automatic
control into soft robots demands more generalizable and robust
approaches to actuator safety.
This work proposes a feedback control framework that
ensures safety of a class of soft robot actuators. The framework
employs a model-based supervisor that dynamically saturates
a primary, unspecified, control strategy - which we term thepose controller (Fig. 1(a)). Our work takes inspiration fromother approaches for safe supervisory control in electromechanical systems, where reachability computations are used
to determine when to switch to the supervisor (Zhang et al.
[11]). We demonstrate our framework on a soft robot limb withembedded position and temperature sensing for two thermallystimulated shape memory alloy (SMA) actuators, using two
different pose controllers, in the presence of environmental
contact (Fig. 1(b)-(c)). This task presents a generalizable
challenge since the cause of failure (excess heat) can only
be indirectly monitored and controlled.

II. F RAMEWORK OVERVIEW
We consider soft robot actuators that can be modeled asaffine systems, a general class that includes the thermallycontrolled activation of SMA wires (Wertz et al. [9]) as well as
modern data-driven methods that admit linear systems (Bruderet al. [2]). If an individual actuator’s internal state is w ande = [w, 1]⊤ , we assume thean affine-augmented state is w
actuator dynamics are
e + 1) = Aw(k)ew(k+ Bu(k) .

(1)

From linear systems theory, the control input that brings oure SET in one timestep issystem state to a desired setpoint w
e SET − Aw(k))eu(k)SET = B⊤ (BB⊤ )† (w.

(2)

If this system is a monotone control system, in that ua ≤ub ⇒ wa (k + 1) ≤ wb (k + 1), it is intuitive that applying
e <w
e SET . We propose the following“less” control will keep w
controller for the supervisor:
1u(k)M AX = γB⊤ (BB⊤ )† ( (I − . . .
γe M AX − Aw(k))
e(1 − γ)A)w,(3)

where γ ∈ (0, 1) is a tuning parameter, and the SET point has
been adjusted to a MAX point with some manipulation of thesystem model. We can readily prove that the resulting closedloop error dynamics in the form of e(k + 1) = (1 − γ)Ae(k),e −w
e M AX , are stable if the open
where the error is e := w
loop system is stable.

More importantly, we can integrate the supervisor with someother feedback controller on the whole system state x thatincludes the pose dynamics. Denoting the pose controller asv(x), we now close the loop as(u(x(k)) =v(x(k))
if v(x(k)) ≤ uM AX (x(k))
uM AX (x(k)) else(4)where the actuator states are implicitly elements of x. The
closed loop system is in C 0 and is Lipschitz continuous (ifv(x) is so). We arrive at the following theorem.
Theorem 1. For the closed-loop system defined by eqns. (1),(3), (4), consider a polytope S = {e|He ≤ h} where e = 0
is the upper bound. If a maximum invariant set calculation
verifies that S is positively invariant under u = u(k)M AX ,then S is also positively invariant under u = u(x(k)).
ee M AX , and we close the loop
In other words, if w(0)≤wwith u(x(k)), safety verification reduces to the well-known
invariant set calculation using the Pre operator. For SMA
thermal dynamics as given in Wertz et al. [9], we have verified
computationally that S is invariant for any γ ∈ (0, 1).
III. R ESULTS
An implementation of this feedback controller and a resulting hardware test is shown in Fig. 1). We have verified thesebehaviors using multiple different v(x), with the reported tests
using a sliding mode controller motivated by Elahinia andAshrafiuon [3]. With the tuning parameter set at γ = 0.3,the SMA wire temperatures (as measured by an internal
thermocouple per Sabelhaus et al. [7]) remained below amaximum despite forceful interaction with a human operator.
Additional tests have demonstrated this same behavior when
our soft robot limb contacts a wall, or is commanded to reachan infeasible pose.
IV. C ONCLUSION
The supervisory control framework proposed here is able
to maintain safe soft robot actuator states, in the form of thetemperature of an SMA wire, without knowledge of the underlying pose controller or environmental contact conditions.
We anticipate this controller opening new directions for softrobot motions without fear of robot failure or degradation. In
particular, ongoing work seeks to incorporate this controller
into state feedback for a soft walking robot.
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