Michael A. Hopkins

Humanoid locomotion on uneven terrain using the time-varying divergent component of motion

This paper presents a framework for dynamic humanoid locomotion on uneven terrain using a novel time-varying extension to the Divergent Component of Motion (DCM). By varying the natural frequency of the DCM, we are able to achieve generic CoM height trajectories during stepping. The proposed planning algorithm computes admissible DCM reference trajectories given desired ZMP plans for single and double support. This is accomplished using reverse-time integration of the discretized DCM dynamics over a finite time horizon. To account for discontinuities during replanning, linear Model Predictive Control (MPC) is implemented over a short preview window. DCM tracking control is achieved using a time-varying proportional-integral controller based on the Virtual Repellent Point (VRP). The effectiveness of the combined approach is verified in simulation using a 30-DoF model of THOR, a compliant torque-controlled humanoid.

Compliant locomotion using whole-body control and Divergent Component of Motion tracking

This paper presents a compliant locomotion framework for torque-controlled humanoids using model-based whole-body control. In order to stabilize the centroidal dynamics during locomotion, we compute linear momentum rate of change objectives using a novel time-varying controller for the Divergent Component of Motion (DCM). Task-space objectives, including the desired momentum rate of change, are tracked using an efficient quadratic program formulation that computes optimal joint torque setpoints given frictional contact constraints and joint position / torque limits. In order to validate the effectiveness of the proposed approach, we demonstrate push recovery and compliant walking using THOR, a 34 DOF humanoid with series elastic actuation. We discuss details leading to the successful implementation of optimization-based whole-body control on our hardware platform, including the design of a “simple” joint impedance controller that introduces inner-loop velocity feedback into the actuator force controller.

An unlumped model for linear series elastic actuators with ball screw drives

Series elastic actuators are frequently modeled using a conventional lumped mass model which has remained mostly unchanged since their introduction almost two decades ago. The lumped model has served well for early development but more descriptive models are now needed for new actuator designs and control approaches. In this paper we propose a new unlumped model specifically for linear series elastic actuators which uses a rack & pinion conceptualization to intuitively depict the mechanics of a linear ball screw drive. Results from hardware experiments are presented and compared to the predicted simulation results for both the conventional model and the new unlumped model. The results demonstrate that the new unlumped model is significantly more representative of the true actuator dynamics.

Design of a compliant bipedal walking controller for the DARPA Robotics Challenge

This paper provides an overview of the bipedal walking controller implemented on ESCHER, a new torque-controlled humanoid designed by Virginia Tech to compete in the DARPA Robotics Challenge (DRC). The robots compliant control approach relies on an optimization-based inverse dynamics solver proposed in a previous publication. This work presents two unique features to improve stability on soft and uncertain terrain, developed in preparation for the dirt track and stairs task at the DRC Finals. First, a step adjustment algorithm is introduced to modify the swing foot position based on the divergent component of motion (DCM) error. Second, a simple heuristic is introduced to improve stability on compliant surfaces such as dirt and grass by modifying the design of the center of pressure (CoP) trajectory. The proposed approach is validated through DRC-related experiments demonstrating the robots ability to climb stairs and traverse soft terrain.

Design of a series elastic humanoid for the DARPA Robotics Challenge

This paper describes the mechanical design of ESCHER, a series elastic humanoid developed to compete in the DARPA Robotics Challenge (DRC). The design methodology was informed by preliminary experimental results obtained using the THOR humanoid, a prototype platform developed for the DRC Trials, relying heavily on an accurate model of the torque-controlled robot in the Gazebo simulation environment. The redesigned lower body features a unique double actuated knee; by driving the single degree of freedom joint with two identical linear series elastic actuators (SEAs), the lower body is able to meet the necessary speed and torque requirements for locomotion on rough terrain. Experimental results demonstrating ESCHERs ability to step onto a 23 cm block, representative of the stairs task at the DRC Finals, validating the proposed approach. Joint torques measured on the hardware platform approximate those in simulation, validating the proposed design methodology.

Embedded joint-space control of a series elastic humanoid

This paper provides an overview of the embedded joint-space control approach developed for THOR, a new series elastic humanoid. The 60 kg robot features electromechanical linear series elastic actuators (SEAs), enabling low-impedance control of each joint in the lower body via linear to rotary and parallel mechanisms. We present a distributed joint impedance control framework that leverages a custom dual-axis motor controller to track position, velocity, and torque setpoints for each pair of joints. The required actuator forces are tracked using an inner force control loop combining feedforward and PID control with a model-based disturbance observer (DOB). Unlike previous approaches, we utilize an inverse plant model based on the open-loop actuator dynamics to simplify tuning of the cascaded controller by decoupling DOB estimates from the inner loop gains. The effectiveness of the proposed approach is verified through trajectory tracking and dynamic walking experiments conducted on the THOR humanoid utilizing a complementary optimization-based whole-body controller.

Optimization-Based Whole-Body Control of a Series Elastic Humanoid Robot

As whole-body control approaches begin to enter the mainstream of humanoid robotics research, there is a real need to address the challenges and pitfalls encountered in hardware implementations. This paper presents an optimization-based whole-body control framework enabling compliant locomotion on THOR, a 34 degree of freedom humanoid featuring force-controllable series elastic actuators (SEAs). Given desired momentum rates of change, end-effector accelerations, and joint accelerations from a high-level locomotion controller, joint torque setpoints are computed using an efficient quadratic program (QP) formulation designed to solve the floating-base inverse dynamics (ID). Constraints on the centroidal dynamics, frictional contact forces, and joint position/torque limits ensure admissibility of the optimized joint setpoints. The control approach is supported by an electromechanical design that relies on custom linear SEAs and embedded joint controllers to accurately regulate the internal and external force...

Dynamic Walking on Uneven Terrain Using the Time-Varying Divergent Component of Motion

This paper presents a framework for dynamic walking on uneven terrain using a novel time-varying extension of the divergent component of motion (DCM). By varying the natural frequency of the DCM, we are able to achieve generic CoM height trajectories during stepping. The proposed approach computes admissible DCM reference trajectories given desired zero moment point (ZMP) plans for single and double support, permitting both flat-footed and heel-toe walking. Real-time planning is accomplished using reverse-time integration of the discretized DCM dynamics over a finite time horizon. To account for discontinuities during replanning, linear model predictive control (MPC) is implemented over a short preview window, enabling smooth transitions between steps. DCM tracking control is achieved using a time-varying proportional-integral controller based on the virtual repellent point (VRP). The effectiveness of the combined approach is verified in simulation using a 30 DOF model of THOR, a compliant torque-controlled humanoid. We demonstrate dynamic locomotion on uneven terrain and heel-toe walking using a complementary whole-body controller to track the corresponding VRP forces.

Two configurations of series elastic actuators for linearly actuated humanoid robots with large range of motion

We have developed two different configurations of series elastic actuators to be used in the lower body of THOR, a full scale humanoid developed for the DARPA Robotics Challenge. Both designs utilize a ball screw transmission but use different output mechanisms. The THOR-Linear actuator uses a simple lever output while the THOR-Hoekens actuator uses a novel inversion of a Hoekens Linkage. The simpler design of the THOR-Linear actuator makes it well suited for parallel actuation applications while the THOR-Hoekens actuator features a larger range of motion and nearly constant mechanical advantage. In this video, we show early tests of the two actuator designs used in the THOR lower body. The video shows the two actuator designs, their range of motion on THOR, and a series of performance tests.

Team VALOR's ESCHER: A Novel Electromechanical Biped for the DARPA Robotics Challenge: Team VALOR's ESCHER

The Electric Series Compliant Humanoid for Emergency Response (ESCHER) platform represents the culmination of four years of development at Virginia Tech to produce a full sized force controlled humanoid robot capable of operating in unstructured environments. ESCHER’s locomotion capability was demonstrated at the DARPA Robotics Challenge (DRC) Finals when it successfully navigated the 61m loose dirt course. Team VALOR, a Track A team, developed ESCHER leveraging and improving upon bipedal humanoid technologies implemented in previous research efforts, specifically for traversing uneven terrain and sustained untethered operation. This paper presents the hardware platform, software, and control systems developed to field ESCHER at the DRC Finals. ESCHER’s unique features include custom linear series elastic actuators (SEAs) in both single and dual actuator configurations and a whole-body control framework supporting compliant locomotion across variable and shifting terrain. A high-level software system designed using the Robot Operating System (ROS) integrated various open-source packages and interfaced with the existing whole-body motion controller. The paper discusses a detailed analysis of challenges encountered during the competition, along with lessons learned critical for transitioning research contributions to a fielded robot. Empirical data collected before, during, and after the DRC Finals validates ESCHER’s performance in fielded environments.