Frequency-Aware Model Predictive Control

Transferring solutions found by trajectory optimization to robotic hardware remains a challenging task. When the optimization fully exploits the provided model to perform dynamic tasks, the presence of unmodeled dynamics renders the motion infeasible on the real system. Model errors can be a result of model simplifications, but also naturally arise when deploying the robot in unstructured and nondeterministic environments. Predominantly, compliant contacts and actuator dynamics lead to bandwidth limitations. While classical control methods provide tools to synthesize controllers that are robust to a class of model errors, such a notion is missing in modern trajectory optimization, which is solved in the time domain. We propose frequency-shaped cost functions to achieve robust solutions in the context of optimal control for legged robots. Through simulation and hardware experiments we show that motion plans can be made compatible with bandwidth limits set by actuators and contact dynamics. The smoothness of the model predictive solutions can be continuously tuned without compromising the feasibility of the problem. Experiments with the quadrupedal robot ANYmal, which is driven by highly-compliant series elastic actuators, showed significantly improved tracking performance of the planned motion, torque, and force trajectories and enabled the machine to walk robustly on terrain with unmodeled compliance

Online, interactive user guidance for high-dimensional, constrained motion planning

We consider the problem of planning a collision-free path for a high-dimensional robot. Specifically, we suggest a planning framework where a motion-planning algorithm can obtain guidance from a user. In contrast to existing approaches that try to speed up planning by incorporating experiences or demonstrations ahead of planning, we suggest to seek user guidance only when the planner identifies that it ceases to make significant progress towards the goal. Guidance is provided in the form of an intermediate configuration $\hat{q}$, which is used to bias the planner to go through $\hat{q}$. We demonstrate our approach for the case where the planning algorithm is Multi-Heuristic A* (MHA*) and the robot is a 34-DOF humanoid. We show that our approach allows to compute highly-constrained paths with little domain knowledge. Without our approach, solving such problems requires carefully-crafting domain-dependent heuristics

Online, interactive user guidance for high-dimensional, constrained motion planning

We consider the problem of planning a collision-free path for a high-dimensional robot. Specifically, we suggest a planning framework where a motion-planning algorithm can obtain guidance from a user. In contrast to existing approaches that try to speed up planning by incorporating experiences or demonstrations ahead of planning, we suggest to seek user guidance only when the planner identifies that it ceases to make significant progress towards the goal. Guidance is provided in the form of an intermediate configuration $\hat{q}$, which is used to bias the planner to go through $\hat{q}$. We demonstrate our approach for the case where the planning algorithm is Multi-Heuristic A* (MHA*) and the robot is a 34-DOF humanoid. We show that our approach allows to compute highly-constrained paths with little domain knowledge. Without our approach, solving such problems requires carefully-crafting domain-dependent heuristics

Bipedal Hopping: Reduced-order Model Embedding via Optimization-based Control

This paper presents the design and validation of controlling hopping on the 3D bipedal robot Cassie. A spring-mass model is identified from the kinematics and compliance of the robot. The spring stiffness and damping are encapsulated by the leg length, thus actuating the leg length can create and control hopping behaviors. Trajectory optimization via direct collocation is performed on the spring-mass model to plan jumping and landing motions. The leg length trajectories are utilized as desired outputs to synthesize a control Lyapunov function based quadratic program (CLF-QP). Centroidal angular momentum, taking as an addition output in the CLF-QP, is also stabilized in the jumping phase to prevent whole body rotation in the underactuated flight phase. The solution to the CLF-QP is a nonlinear feedback control law that achieves dynamic jumping behaviors on bipedal robots with compliance. The framework presented in this paper is verified experimentally on the bipedal robot Cassie.Comment: 8 pages, 7 figures, accepted by IROS 201

When and Where to Step: Terrain-Aware Real-Time Footstep Location and Timing Optimization for Bipedal Robots

Online footstep planning is essential for bipedal walking robots, allowing them to walk in the presence of disturbances and sensory noise. Most of the literature on the topic has focused on optimizing the footstep placement while keeping the step timing constant. In this work, we introduce a footstep planner capable of optimizing footstep placement and step time online. The proposed planner, consisting of an Interior Point Optimizer (IPOPT) and an optimizer based on Augmented Lagrangian (AL) method with analytical gradient descent, solves the full dynamics of the Linear Inverted Pendulum (LIP) model in real time to optimize for footstep location as well as step timing at the rate of 200~Hz. We show that such asynchronous real-time optimization with the AL method (ARTO-AL) provides the required robustness and speed for successful online footstep planning. Furthermore, ARTO-AL can be extended to plan footsteps in 3D, allowing terrain-aware footstep planning on uneven terrains. Compared to an algorithm with no footstep time adaptation, our proposed ARTO-AL demonstrates increased stability in simulated walking experiments as it can resist pushes on flat ground and on a $10^{\circ}$ ramp up to 120 N and 100 N respectively. For the video, see https://youtu.be/ABdnvPqCUu4. For code, see https://github.com/WangKeAlchemist/ARTO-AL/tree/master.Comment: 32 pages, 15 figures. Submitted to Robotics and Autonomous System

UAV/UGV Autonomous Cooperation: UAV Assists UGV to Climb a Cliff by Attaching a Tether

This paper proposes a novel cooperative system for an Unmanned Aerial Vehicle (UAV) and an Unmanned Ground Vehicle (UGV) which utilizes the UAV not only as a flying sensor but also as a tether attachment device. Two robots are connected with a tether, allowing the UAV to anchor the tether to a structure located at the top of a steep terrain, impossible to reach for UGVs. Thus, enhancing the poor traversability of the UGV by not only providing a wider range of scanning and mapping from the air, but also by allowing the UGV to climb steep terrains with the winding of the tether. In addition, we present an autonomous framework for the collaborative navigation and tether attachment in an unknown environment. The UAV employs visual inertial navigation with 3D voxel mapping and obstacle avoidance planning. The UGV makes use of the voxel map and generates an elevation map to execute path planning based on a traversability analysis. Furthermore, we compared the pros and cons of possible methods for the tether anchoring from multiple points of view. To increase the probability of successful anchoring, we evaluated the anchoring strategy with an experiment. Finally, the feasibility and capability of our proposed system were demonstrated by an autonomous mission experiment in the field with an obstacle and a cliff.Comment: 7 pages, 8 figures, accepted to 2019 International Conference on Robotics & Automation. Video: https://youtu.be/UzTT8Ckjz1