IEEE Robotics & Automation Magazine - December 2015 - 38

In general, the goal is to design the dynamic behavior of
the robot, which is described as mechanical impedance shaping in [4]. A further differentiation concerns active and passive compliance. Active compliance expresses that the behavior is generated by a control system [5], while passive
compliance refers to inherent compliance properties of the
robot mechanism itself [6].
The active impedance control formulation [5], [7], [8]
shows excellent performance and has already found its way
into industrial applications [9], [10]. However, there are limitations for impacts and actuator efficiency. The implementation of passive impedance draws more open questions, and
over the years, mechanisms at various levels and scales have
been considered. Attempts to increase the interaction performance of industrial robots have mechanically incorporated
compliant elements at the tool center point (TCP). A popular
example is the remote center of compliance (RCC) [11].
Artificial muscle actuation concepts with different actuator
technologies have been applied to robots [12]-[14] and
improved the mechanical modulation of the impedance
parameters [6], [15], [13], [16]. Variable stiffness actuators
(VSAs) [17], [18] provide beneficial properties to increase
the performance. The major advantages of VSAs are the
higher robustness with respect to impacts [19], better energy
efficiency [20], extended dynamic capability [21], [22], and
their improved task adaptability [23] due to their adjustable
stiffness. In fact, these attributes of compliance also represent
the main reasons why humans still have an unreachable performance compared with their robotic counterparts.
Some of the classical torque-controlled robotic systems
developed in the past show excellent performance. Two
names in the class of torque-controlled robots are the DLRKUKA lightweight robot (LWR 3) [24] and the Sarcos Primus humanoid [25]. Being able to utilize research and development results from torque-controlled robots is a big
advantage of VSA systems. The capability to estimate the
joint torques from the elongation of the elastic elements [26]
enables the application of advanced torque-control-based
methods. Yet the system complexity of VSA robots, particularly of the nonlinear elastic elements and characterized by
low-damped oscillatory behavior, requires more sophisticated control methods.
In this article, we will generalize well-established torque
control methods developed in the flexible joint context to
variable stiffness robots, such as the DLR HASy [27], as
shown in Figure 1. Our main contributions are the adaptation
of the concepts to VSA robots, the experimental validation,
and the discussions on practical applications. The aim is to be
able to provide a comprehensive set of controllers suitable for
VSA robots to the user.
Vsas and the Dlr Hasy
VSA Setup
Many different VSA joint designs have been presented
over the years. The main functionalities of the joints are
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DECEMBER 2015

similar as they enable the simultaneous adaptation of joint
torque and impedance parameters. The differences are
related to mechanical solutions for adjusting those quantities [29]. Therefore, it is appropriate to treat a possibly
large class of joints from an abstract point of view [30]. In
the following section, we focus on the development of
algorithms for a certain class of actuators. This restriction
does not limit the generality of the presented methods, as
they can be easily adapted to any VSA joints that fit into
the dynamic modeling approach from the "VSA Modeling" section.
The electric motor is the power plant of choice of the
most robotic arms, due to the ease of torque control, high
bandwidth, and high power density in combination with a
gear box. However, they cannot be considered ideal torque
sources, since high reduction ratio designs are usually limited by nonback driveability, which results in limited
intrinsic compliance. The class of VSAs considered here
realizes this compliance by a variable, nonlinear, elastic element mounted between motor and link. The active stiffness variation is achieved by an additional motor, the stiffness adjuster, which allows the variation of the internal
stiffness mechanism to change the stiffness characteristic,
as shown in Figure 2(a). A particular aspect of VSAs is that
the stiffness variation mechanism adds an additional
degree of freedom (DOF) to the joint and, therefore,
increases the system and control complexity. To be energy
efficient, able to deliberately dissipate kinetic energy, and
capable of utilizing the elastic elements to measure joint
torques, the joints are designed with very low intrinsic
damping . However, this process is demanding for mechanical joint design as friction effects at the link and spring
mechanism have to be minimized. Joint damping, if
required in the application, is almost exclusively reached
through control, as explained in the "State Feedback
Damping Control" section. Such a joint setup, which eliminates an additional mechanical damping solution [31],
greatly reduces the mechanical complexity.
VSA Modeling
The VSA joint characteristics with a nonlinear and variable
spring torque function can be described by
x

= f ({, v),

(1)

where x is the joint torque, { is the joint deflection, and v is
the stiffness variation parameter. In general, the torquedeflection curve can be an arbitrary shape, but two characteristics are most commonly applied: 1) a linearly variable stiffness profile x = k (v) {, where k (v) is the stiffness [32], [33]
and 2) a progressive (2f/2{ > 0, 2 3 f/2{ 3 > 0) profile for all
v [34], [35] [see Figure 2(c)]. The latter results in increasingly
repellent forces for increasing joint deflections, and thereby, it
prevents the joint from running into its end stops while still
maintaining a smooth stiffness change.



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