Realizing Dynamic and Efficient Bipedal Locomotion on the Humanoid Robot DURUS Jacob Reher1, Eric A. Cousineau2, Ayonga Hereid1, Christian M. Hubicki1, and Aaron D. Ames3 Abstract— This paper presents the methodology used to achieve efficient and dynamic walking behaviors on the pro- totype humanoid robotics platform, DURUS. As a means of providing a hardware platform capable of these behaviors, the design of DURUS combines highly efficient electromechanical components with “control in the loop” design of the leg morphology. Utilizing the final design of DURUS, a formal framework for the generation of dynamic walking gaits which maximizes efficiency by exploiting the full body dynamics of the robot, including the interplay between the passive and active elements, is developed. The gaits generated through this methodology form the basis of the control implementation experimentally realized on DURUS; in particular, the trajec- tories generated through the formal framework yield a feed- forward control input which is modulated by feedback in the form of regulators that compensate for discrepancies between the model and physical system. The end result of the unified approach to control-informed mechanical design, formal gait design and regulator-based feedback control implementation is efficient and dynamic locomotion on the humanoid robot DU- RUS. In particular, DURUS was able to demonstrate dynamic Fig. 1: Humanoid robot DURUS exhibiting dynamic walking locomotion at the DRC Finals Endurance Test, walking for just under five hours in a single day, traveling 3.9 km with a mean behaviors at the DARPA Robotics Challenge Endurance Test. cost of transport of 1.61—the lowest reported cost of transport achieved on a bipedal humanoid robot. I. INTRODUCTION Traditional approaches for locomotion prioritize the ability to complete a wide-variety of tasks, e.g., step placement, The humanoid robot, DURUS, was revealed to the public turning, and stair climbing, over achieving highly dynamic at the DARPA Robotics Challenge (DRC) Robot Endurance and efficient locomotion. At the core of most methods em- Test in June 2015 [1]. Developed by SRI International, ployed on robots today is a low-dimensional representation DURUS was designed with the overarching goal of achieving of the full-order robot which utilizes a heuristic notion of never before seen efficiency in locomotion, thereby allowing stability known as the Zero Moment Point (ZMP) criterion for longer autonomous battery-powered operation. This goal [16], [25], and an extension termed Capture Point [20]. is in response to the current state of the art in humanoid The ZMP and capture point methods are robust and allow robots. While there have been dramatic increases in capa- for a variety of walking behaviors; however, the resulting bilities for performing tasks and navigating terrain through locomotion is typically slow and very energy consuming. semi-autonomous task-based operation—as seen in the DRC More recently, there have been several optimization based Finals—this is often achieved at the cost of increased energy controllers [10], [17], [8], [9], [24] proposed in response to usage. The results presented in this paper take the opposite the DARPA Robotics Challenge. However, these approaches perspective by prioritizing a single objective: achieve max- have been applied mainly with ZMP and capture point imum efficiency in locomotion through a holistic design, heuristics coupled with constraints, offer no formal guaran- control and implementation methodology, with a focus on tees, and again lack efficiency. With a view towards creating utilizing the full body dynamics of the robot—leveraging highly efficient walking, the passive dynamics community passive mechanical elements—to realize dynamic walking. [18], [6], [4], [28] has aimed to utilize the passive dynamics This work is supported by the DARPA M3A Program and NSF grants of the robot to attain efficient walking with minimal power CPS-1239055, NRI-1526519 injection from actuators. While these walkers can achieve 1 Jacob Reher, Ayonga Hereid, and Christian M. Hubicki are with the very efficient walking, e.g., the Cornell Ranger has the lowest Woodruff School of Mechanical Engineering, Georgia Institute of Technol- ogy, Atlanta, GA, 30332 USA recorded cost of transport for a legged robot of 0:19 [5], the 2Eric Cousineau is with Mathworks Inc. and is a previous member of the design typically involves the use of many passive elements AMBER Lab such as free-swinging joints and small actuators which make 3Aaron D. Ames is with the Woodruff School of Mechanical Engineering and the School of Electrical and Computer Engineering, Georgia Institute implementation difficult on a robot which must also have the of Technology, Atlanta, GA, 30332, USA ability to locomote and still perform a variety tasks. Absolute encoder Cycloidal discs Needle roller bearings Cross roller bearing Chain BLDC Electric reduction Motor Suspension Ankle pivot bushings Coil Fig. 2: Approach to implementing efficient locomotion on springs Bottom-out bumpers DURUS. Specifically, a formally stable walking gait is used Optional foot for time-based position tracking on hardware. A regulator pivot structure then perturbs the trajectories on the torso roll, hip roll, and hip yaw joints for stabilization. Fig. 3: Novel mechanical components used on DURUS in order to improve efficiency in locomotion. This paper presents the methods used to demonstrate dy- namic and efficient walking on the humanoid robot, DURUS, basis for which the control strategy builds upon, is described experimentally. This methodology begins with the design in Sec. II. The mathematical modeling of DURUS is pre- of dynamic and efficient walking gaits on bipedal robots sented in Sec. III. The control approach, including the formal through hybrid zero dynamics (HZD) [2], [12], [15], [26], feedforward gait construction and the feedback regulator [27], a mathematical framework that utilizes hybrid systems structure are detailed in Sec. IV. Finally, the experimental models coupled with nonlinear controllers that provably results are presented in Sec. V. results in stable locomotion. In particular, we utilize HZD to II. DESIGN formulate a nonlinear optimization problem for DURUS that The underlying mechanical and electrical components accounts for the full-body dynamics of the robot in order incorporated into the design of DURUS provide an essen- to maximize the efficiency of the gait. The end result is tial foundation from which the control design can build a nonlinear controller that provably produces stable robotic upon. In particular, a two-pronged approach was taken in walking [2]. The resulting trajectories are realized on the the design of DURUS: (1) novel mechanical and electrical hardware via a feedforward term that encodes the formal components providing significant gains in efficiency and (2) a gait design. To account for differences between the physical leg morphology which was the result of an iterative feedback robot and the ideal model, a heuristic feedback is added to loop between mechanical design and control synthesis. The the control implementation in the form of regulators that components resulting from this approach are shown in Fig. 3. modulate joints based upon environmental perturbations. The control framework presented allows for the full utilization Novel Components. The primary mechanical components of novel mechanical components on DURUS, including: which provided gains in overall efficiency were the actua- efficient cycloidal gearboxes which allow for almost lossless tor and transmission elements (see Fig. 3). Each actuator- transmission of power and compliant elements at the ankles gearbox combination consisted of an electric motor con- for absorbing the impacts at foot-strike. nected via a chain reduction to a custom-designed cycloid At the core of the control architecture implemented on transmission, which can achieve up to 97% efficiency. Each DURUS is the underlying assumption that the dynamics actuator-gearbox unit was lightweight, weighing only 2:7 kg of the electromechanical system will operate near those of and able to output 250 Nm of torque with maximum joint 2 the desired system. The low-level motor controllers of the accelerations exceeding 130 rad/s . robot ensure that the formally generated trajectories will To ultimately realize dynamic and efficient locomotion on be closely tracked, with 0:005 rad rms tracking error for the humanoid robot DURUS, precision in control implemen- the experiments documented in this paper. Also, due to tation is required at every level of the hardware. Therefore, an the relatively small stabilizing perturbations induced by the essential component in the process of realizing locomotion is feedback regulators, the walking trajectories demonstrated a motor controller which can accurately track the trajectories on DURUS in this work are shown to preserve 83:3% of generated in Sec. IV accurately. Custom motor controllers the “formal” gait. Additionally, through the combination are employed on DURUS, allowing for 10 kHz control of of formal controller design and novel mechanical design, torque, current, and position. For the duration of the walking the humanoid robot DURUS was able to achieve a mean analyzed in Sec. V, these motor controllers tracked joint electrical cost of transport of 1:61 over roughly five hours positions with an overall rms error of 0:005 rad and a peak of continuous walking—the lowest recorded electrical cost error of 0:026 rad. Additionally, DURUS is self-powered of transport for a bipedal humanoid robot. with a 1:1 kWh battery pack weighing 9:5 kg. The presented work is structured as follows: The overview Control in the Loop Design. The morphology of DURUS, of the mechanical components, which provide an efficient and specifically the role of passive-compliant elements, di- Electromechanical Design Iter. 0 Iter. 1 Iter. 2 Iter. 3 Iter. 6 Simulation Fig. 4: Iterative design process which facilitated a leg mor- phology satisfying hardware constraints in simulation. Fig. 5: The coordinate system used on DURUS. rectly impacted how well a control scheme could achieve III. ROBOT MODEL efficient and stable dynamic gaits both in simulation and experimentally.