Short Description:

Traditional robots today (such as the ones used in factories) have a fixed base and are fully actuated under their operating conditions. However, modern robots inspired by animals (such as hoppers, quadruped, humanoids) are not bound to one place and are always under-actuated. Like animals, these robots can perform dynamic movements, demonstrate compliance, and are robust to contact during their movements. Robots of the future will be able to move more dynamically and safely in a rugged environment shared with humans. To realize this future, the underactuated lab aims to develop a thorough understanding of the problem by identifying and developing key canonical robotic systems and gradually increasing the system complexity to address open problems in the areas of dynamic legged locomotion, dexterous manipulation, agile flight, etc. The approach is inspired by studying optimality principles in analytical mechanics, mechanical design, and control of robotic systems. This lab will benefit not only in the research and development of new physically intelligent robots but also in developing teaching aids for robotics and artificial intelligence (AI) courses.  

What are Underactuated Systems?  

With underactuated, we refer to robotic systems that cannot actuate every available degree of freedom (DoF) in general or at a given moment in time. There are multiple reasons for underactuation. For example, systems with fewer actuators than independent DoF such as humanoid robots, aerial drones, swimming robots, etc. are trivially underactuated. Another case would be a system with an equal number of actuators as degrees of freedom, but due to state or torque limits, it is still not possible to move the system instantly in a certain direction. This makes all possible robotic systems underactuated.   
 Examples of Underactuated Systems
For example, a double pendulum with one actuated and one passive joint would be underactuated, because it has two independent DOFs, but only one of them can be controlled. If the shoulder/first joint is not actuated, this system is traditionally called an Acrobot. An electric car with two motors and a steering wheel has three actuators and three DOFs, assuming it moves on a plane. A person driving the car may navigate it to any desired position on the surface by making turns. However, the car cannot be moved directly sideways due to the limits of the steering axis in a traditional car, a feature that would come in very handy when parking the vehicle (and eliminate the parallel parking problem). Another case is underactuation due to the torque limits of the actuators.  

Why study underactuation?

The problem of underactuation is often addressed by ad-hoc workarounds in the robotics community. For example, to carry large payloads we often rely on exceedingly powerful and rigid robotic manipulators and use feedback control to override their natural dynamics. However, this trick does not come without its drawbacks. One apparent drawback is that industrial manipulators are stiff position-controlled systems, which makes them potentially dangerous for safe human-robot interaction. In fact, if we think more closely about the problem, even those systems are still underactuated, due to limited joint accelerations. As physics teaches us, infinite acceleration of a mass requires infinite energy, which we cannot provide even with bulky actuators. On the contrary, in nature, system dynamics are exploited in intelligent ways for coming up with optimal control strategies. For example, in acrobatics, a human can lift its body weight to a swing-up configuration by intelligently harnessing energy through multiple swings even though the torque available in the human wrist is not sufficient to directly draw the human body to an upside-down configuration.

Underactuated Lab at DFKI Robotics Innovation Center

The goal of the Underactuated Lab is to develop simple, capable, and robust robotic systems. We aim to build underactuated systems that can achieve equal or superior behavior than existing fully actuated systems. The only way to meet this goal is by exploiting the system dynamics in physically intelligent ways instead of being stiff to cancel them out. While such a dynamic control introduces new challenges to our understanding of robotics, it promises the emergence of a new generation of more nimble and agile robots.

Lab Infrastructure

The lab has successfully implemented hardware and software for three different canonical systems: Torque Limited Simple Pendulum, Double Pendulum (Acrobot/Pendubot), and Single Hopping Leg (which can hop and perform backflips).

The torque-limited simple pendulum is the most basic underactuated system. It has one actuator and only one DoF, but can still be considered underactuated due to torque limitation. The actuator requires approximately 2.5 Nm to lift a mass of 0.5 kg attached to a 0.5-meter lever to the top position, whereas in our experiments the actuator torque is limited to 1 Nm. In order to still lift the mass into the top position, we generate trajectories for a dynamical swing up with a range of optimal control methods and machine learning approaches. The platform can serve as an educational and research tool for getting started into underactuated robotics. The entire hardware and software platform is open source and is available at:

github.com/dfki-ric-underactuated-lab/torque_limited_simple_pendulum