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  1. This paper proposes an online gain adaptation approach to enhance the robustness of whole-body control (WBC) framework for legged robots under unknown external force disturbances. Without properly accounting for external forces, the closed-loop control system incorporating WBC may become unstable, and therefore the desired task goals may not be achievable. To study the effects of external disturbances, we analyze the behavior of our current WBC framework via the use of both full-body and centroidal dynamics. In turn, we propose a way to adapt feedback gains for stabilizing the controlled system automatically. Based on model approximations and stability theory, we propose three conditions to ensure that the adjusted gains are suitable for stabilizing a robot under WBC. The proposed approach has four contributions. We make it possible to estimate the unknown disturbances without force/torque sensors. We then compute adaptive gains based on theoretic stability analysis incorporating the unknown forces at the joint actuation level. We demonstrate that the proposed method reduces task tracking errors under the effect of external forces on the robot. In addition, the proposed method is easy-to-use without further modifications of the controllers and task specifications. The resulting gain adaptation process is able to run in real-time. Finally, we verify the effectiveness of our method both in simulations and experiments using the bipedal robot Draco2 and the humanoid robot Valkyrie . 
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  2. We propose a locomotion framework for bipedal robots consisting of a new motion planning method, dubbed trajectory optimization for walking robots plus (TOWR+), and a new whole-body control method, dubbed implicit hierarchical whole-body controller (IHWBC). For versatility, we consider the use of a composite rigid body (CRB) model to optimize the robot’s walking behavior. The proposed CRB model considers the floating base dynamics while accounting for the effects of the heavy distal mass of humanoids using a pre-trained centroidal inertia network. TOWR+ leverages the phase-based parameterization of its precursor, TOWR, and optimizes for base and end-effectors motions, feet contact wrenches, as well as contact timing and locations without the need to solve a complementary problem or integer program. The use of IHWBC enforces unilateral contact constraints (i.e., non-slip and non-penetration constraints) and a task hierarchy through the cost function, relaxing contact constraints and providing an implicit hierarchy between tasks. This controller provides additional flexibility and smooth task and contact transitions as applied to our 10 degree-of-freedom, line-feet biped robot DRACO. In addition, we introduce a new open-source and light-weight software architecture, dubbed planning and control (PnC), that implements and combines TOWR+ and IHWBC. PnC provides modularity, versatility, and scalability so that the provided modules can be interchanged with other motion planners and whole-body controllers and tested in an end-to-end manner. In the experimental section, we first analyze the performance of TOWR+ using various bipeds. We then demonstrate balancing behaviors on the DRACO hardware using the proposed IHWBC method. Finally, we integrate TOWR+ and IHWBC and demonstrate step-and-stop behaviors on the DRACO hardware. 
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  3. This paper proposes a method to generate feasible trajectories for robotic systems with predefined sequences of switched contacts. The proposed trajectory generation method relies on sampling-based methods, optimal control, and reach-ability analysis. In particular, the proposed method is able to quickly test whether a simplified model-based planner, such as the Time-to-Velocity-Reversal planner, provides a reachable contact location based on reachability analysis of the multi-body robot system. When the contact location is reachable, we generate a feasible trajectory to change the contact mode of the robotic system smoothly. To perform reachability analysis efficiently, we devise a method to compute forward and backward reachable sets based on element-wise optimization over a finite time horizon. Then, we compute robot trajectories by employing optimal control. The main contributions of this study are the following. Firstly, we guarantee whether planned contact locations via simplified models are feasible by the robot system. Secondly, we generate optimal trajectories subject to various constraints given a feasible contact sequence. Lastly, we improve the efficiency of computing reachable sets for a class of constrained nonlinear systems by incorporating bi-directional propagation (forward and backward). To validate our methods we perform numerical simulations applied to a humanoid robot walking. 
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  4. Whole-body control (WBC) is a generic task-oriented control method for feedback control of loco-manipulation behaviors in humanoid robots. The combination of WBC and model-based walking controllers has been widely utilized in various humanoid robots. However, to date, the WBC method has not been employed for unsupported passive-ankle dynamic locomotion. As such, in this article, we devise a new WBC, dubbed the whole-body locomotion controller (WBLC), that can achieve experimental dynamic walking on unsupported passive-ankle biped robots. A key aspect of WBLC is the relaxation of contact constraints such that the control commands produce reduced jerk when switching foot contacts. To achieve robust dynamic locomotion, we conduct an in-depth analysis of uncertainty for our dynamic walking algorithm called the time-to-velocity-reversal (TVR) planner. The uncertainty study is fundamental as it allows us to improve the control algorithms and mechanical structure of our robot to fulfill the tolerated uncertainty. In addition, we conduct extensive experimentation for: (1) unsupported dynamic balancing (i.e., in-place stepping) with a six-degree-of-freedom biped, Mercury; (2) unsupported directional walking with Mercury; (3) walking over an irregular and slippery terrain with Mercury; and 4) in-place walking with our newly designed ten-DoF viscoelastic liquid-cooled biped, DRACO. Overall, the main contributions of this work are on: (a) achieving various modalities of unsupported dynamic locomotion of passive-ankle bipeds using a WBLC controller and a TVR planner; (b) conducting an uncertainty analysis to improve the mechanical structure and the controllers of Mercury; and (c) devising a whole-body control strategy that reduces movement jerk during walking. 
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  5. We present a method that finds locomanipulation plans that perform simultaneous locomotion and manipulation of objects for a desired end-effector trajectory. Key to our approach is to consider an injective locomotion constraint manifold that defines the locomotion scheme of the robot and then using this constraint manifold to search for admissible manipulation trajectories. The problem is formulated as a weighted-A* graph search whose planner output is a sequence of contact transitions and a path progression trajectory to construct the whole-body kinodynamic locomanipulation plan. We also provide a method for computing, visualizing, and learning the locomanipulability region, which is used to efficiently evaluate the edge transition feasibility during the graph search. Numerical simulations are performed with the NASA Valkyrie robot platform that utilizes a dynamic locomotion approach, called the divergent-component-of-motion (DCM), on two example locomanipulation scenarios. 
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  6. In this work, we propose a trajectory generation method for robotic systems with contact force constraint based on optimal control and reachability analysis. Normally, the dynamics and constraints of the contact-constrained robot are nonlinear and coupled to each other. Instead of linearizing the model and constraints, we directly solve the optimal control problem to obtain the feasible state trajectory and the control input of the system. A tractable optimal control problem is formulated which is addressed by dual approaches, which are sampling-based dynamic programming and rigorous reachability analysis. The sampling-based method and Partially Observable Markov Decision Process (POMDP) are used to break down the end-to-end trajectory generation problem via sample-wise optimization in terms of given conditions. The result generates sequential pairs of subregions to be passed to reach the final goal. The reachability analysis ensures that we will find at least one trajectory starting from a given initial state and going through a sequence of subregions. The distinctive contributions of our method are to enable handling the intricate contact constraint coupled with system’s dynamics due to the reduction of computational complexity of the algorithm. We validate our method using extensive numerical simulations with a legged robot. 
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  7. This paper describes the control, and evaluation of a new human-scaled biped robot with liquid cooled viscoelastic actuators (VLCA). Based on the lessons learned from previous work from our team on VLCA, we present a new system design embodying a Reaction Force Sensing Series Elastic Actuator and a Force Sensing Series Elastic Actuator. These designs are aimed at reducing the size and weight of the robot’s actuation system while inheriting the advantages of our designs such as energy efficiency, torque density, impact resistance and position/force controllability. The robot design takes into consideration human-inspired kinematics and range-of-motion, while relying on foot placement to balance. In terms of actuator control, we perform a stability analysis on a Disturbance Observer designed for force control. We then evaluate various position control algorithms both in the time and frequency domains for our VLCA actuators. Having the low level baseline established, we first perform a controller evaluation on the legs using Operational Space Control. Finally, we move on to evaluating the full bipedal robot by accomplishing unsupported dynamic walking. 
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