Model Predictive Control for Pneumatically Actuated Soft Robots

Traditional rigid robots, like those used in manufacturing, have been effective at precise, accurate, rapid motions in well structured environments for many decades now. However, they operate largely behind cages due to the danger of injury when moving in close proximity to people. A significant and recent shift in robotics involves trading rigid links and rigid actuators for soft, deformable links and compliant actuators. These “soft robots” generally have lower inertia and avoid many problems caused by a high effective inertia resulting from high gear ratios necessary for rigid robots. This shift to soft robots will allow robots to safely operate in close proximity to humans. Design of such soft robots, which has been a major emphasis in research, does not completely enable soft robots to effectively perform tasks. The focus of this article is the development of dynamic models and control methods to allow multi-degree of freedom soft robots to perform useful tasks. We present results on fully inflatable, pneumatically actuated, soft robot platforms which include a fourteen degree of freedom humanoid robot. I. BENEFITS OF SOFT ROBOTS There has been significant interest in making robots more effective at interacting with humans and operating in human environments. Robots currently have limited uses in homes, hospitals, schools, or other areas where safe interaction with people or the environment may be necessary. One reason why robots are not common in these places is because traditional robots can be dangerous to people or property when there is incidental contact. Benefits from soft robot platforms like the one we describe for control development in this article include the fact that the compliance comes from passive elements (air) instead of requiring active sensors and controllers for added safety. In addition, we control the robot at fairly low pressures including 6.9-13.8 kPa (1-2 PSI) gauge in the main body chamber and 172.4 kPa (25 PSI) gauge in the actuation bladders. In comparison, these pressures are less than a bike tire, which ranges from 206.8 to 896.3 kPa (30-130 PSI). This means there is lower risk of injury when there is failure such as bursting or leaking of air. In addition to compliance, lightweight robots, such as the platform for which we present results, have less inertia and are less likely to cause bodily harm because of lower contact forces and lower overall momentum when moving at varying speeds. Finally, this specific platform can be contained in a very small packing volume when deflated. This combination of low-weight and small packing volume is very beneficial for applications where the cost of larger and heavier robots becomes prohibitive such as in space or even search and rescue operations. Our research is motivated by a desire to take advantage of the positive These authors are in alphabetical order and all authors are affiliated with Brigham Young University characteristics of soft and inflatable robotic systems while maintaining a level of control that will allow them to be useful. Applications for a robot of this type include search and rescue, health care, assistance with activities of daily living, and space exploration. In this article we present dynamic models and control methods for soft robots. Our results show the feasibility of an approach that is considerably different than most current soft robotics research for manipulation since the complete structure and actuation of our robot comes entirely from air instead of any rigid links or cable driven actuators. Although control of our fabric-based, pneumatically actuated soft robots is a particularly difficult problem, we present encouraging and repeatable results. Fig. 1: This is a fourteen degree of freedom soft robot named King Louie with no rigid internal structure. II. PAST RELATED RESEARCH ON SOFT ROBOTS AND CONTROL In [1], lightweight structures are listed as a desirable design characteristic for a soft robot. The soft robots we use in this paper are at least an order of magnitude lighter than most multi-degree of freedom robots, even those previously referenced as “lightweight” in [1], since the entire humanoid robot (not including the pneumatic control valves) has a mass of approximately 13.6 kg (30 lbs). Similar past research to that presented in this article can be divided into two main areas. First, control methods for other soft robots, and second, past applications of a specific type of optimal control that we are using called model predictive control. A. Controlling Soft Robots Our soft robot platform is a pneumatically actuated, inflatable robot which is lightweight and has a high strength-toweight ratio. Related to this fabric-based test bed, there has been significant amounts of work in developing materials, sensors, structures, and actuators that are lightweight and compliant. These materials are often inspired by biological systems and many are discussed in the literature [2]. Past research involving inflatable robots has mostly looked at the design and performance of an actuator or a series of actuators. In our research, we show that an entire system can be inflatable and control methods can be developed for the system to effectively complete tasks normally done by a robot with rigid structure. The lack of literature on the control of inflatable structures where there is a wide range of applications suggests a novel and important area of robotics research. In previous work on controlling soft robots, researchers were able to limit contact forces using inflatable links with cable tendon and DC servo motor actuators [3], [4]. While cable driven actuators are an effective means of actuation for inflatable structures, our work has focused on using antagonistic pneumatic bladders which are more consistent with the design intent of completely inflatable structures. In [5], [6], and [7], using an actuation method similar to what is described within this article, it was found that motion planning was possible for fluid driven elastomer actuators using dynamic models and constant curvature kinematics. However, although they use multiple degrees of freedom, the manipulator motion is restricted to two dimensions in a plane. Additionally, in order to reach specific locations they require learning a new control policy. Also similar to our work is research that uses rotary elastic chamber actuators such as in [8] and [9], where two antagonistic bellows impart torque on an armature rotating about a rigid rotary joint. However, these compliant joints and their benefits are limited by the fact that they are still connected by rigid, higher inertia links. A major improvement in the results we present in this article is that previously (see [10]) we modeled torque on an inflatable joint with a linear impedance model. This model included a mapping between a desired joint angle and corresponding equilibrium pressures. This mapping overly simplified the model from two individual actuation chamber pressures for each joint to representing actuation pressures as a single input. In preliminary work with a single degree of freedom we showed that including actuation pressures as state variables significantly improved performance and allowed us to control position and stiffness simultaneously, (see [11]). In this article, we show how we identified new models that related pressure in the antagonistic actuation chambers to torque applied at the joint. We show significant improvement in performance as compared to our past results in [10] and quantify repeatability for a multi-degree of freedom soft robot manipulator unlike in [11]. We expect that relating torque to pressure on an individual link by link basis will allow us to more accurately model joint coupling in future work. B. Model Predictive Control for Robotics The fact that for our hardware platform have two control inputs for each joint (i.e. the dynamics between the states and inputs are coupled) makes traditional PID or other singleinput, single-output (SISO) control methods less applicable. The SISO designation simply means that a dynamic system has one control input and one state variable or output of interest. Instead we use a model-based control method called model predictive control (MPC). MPC is a form of optimal control that has long been used in the chemical processing industry. The main idea is that we can minimize a cost function over a finite time horizon subject to the dynamics of our system expressed as an equality constraint. This is similar in many ways to a Linear Quadratic Regulator (LQR) with a finite horizon. However, there are two major differences. The first difference is that we often include other constraints on the states and inputs that are useful in either describing real limitations or in forcing certain states to be within userdefined limits. The second difference between MPC and LQR is that we solve this optimization for every time step that the controller is running and apply only the first resultant control input. This allows us to update the system model, constraints and disturbances in order to get some of the benefits of both closed-loop feedback control and optimal control. Recent advances in computing power and dynamic optimization techniques such as those presented in [12] have made MPC a viable control method in applications that require a high control rate. MPC has been demonstrated in robotics applications including control of unmanned aerial & surface vehicles, [13], [14], [15] and more recently in robot manipulation with rigid links [16], [17], [18], [19]. III. SOFT ROBOT TESTBEDS The platforms used for this research include a fourteen degree of freedom humanoid robot called King Louie (see Figure 1) and a single degree of freedom joint called a “grub” (see Figure 2). Both were developed and built by Pneubotics, an affiliate of Otherlab. The robot platforms are based on the designs for rotary, fabric-based, pneumatic actuated