Distributed Collision-Free Motion Coordination on a Sphere: A Conic Control Barrier Function Approach

This letter studies a distributed collision avoidance control problem for a group of rigid bodies on a sphere. A rigid body network, consisting of multiple rigid bodies constrained to a spherical surface and an interconnection topology, is first formulated. In this formulation, it is shown that motion coordination on a sphere is equivalent to attitude coordination on the 3-dimensional Special Orthogonal group. Then, an angle-based control barrier function that can handle a geodesic distance constraint on a spherical surface is presented. The proposed control barrier function is then extended to a relative motion case and applied to a collision avoidance problem for a rigid body network operating on a sphere. Each rigid body chooses its control input by solving a distributed optimization problem to achieve a nominal distributed motion coordination strategy while satisfying constraints for collision avoidance. The proposed collision-free motion coordination law is validated via simulation

Distributed Collision-Free Motion Coordination on a Sphere: A Conic Control Barrier Function Approach

This letter studies a distributed collision avoidance control problem for a group of rigid bodies on a sphere. A rigid body network, consisting of multiple rigid bodies constrained to a spherical surface and an interconnection topology, is first formulated. In this formulation, it is shown that motion coordination on a sphere is equivalent to attitude coordination on the 3-dimensional Special Orthogonal group. Then, an angle-based control barrier function that can handle a geodesic distance constraint on a spherical surface is presented. The proposed control barrier function is then extended to a relative motion case and applied to a collision avoidance problem for a rigid body network operating on a sphere. Each rigid body chooses its control input by solving a distributed optimization problem to achieve a nominal distributed motion coordination strategy while satisfying constraints for collision avoidance. The proposed collision-free motion coordination law is validated via simulation

Relationship Between Balance Recovery From a Forward Fall and Lower-Limb Rate of Torque Development

The authors examined the relationship between the maximum recoverable lean angle via the tether-release method with early- or late-phase rate of torque development (RTD) and maximum torque of lower-limb muscle groups in 56 young healthy adults. Maximal isometric torque and RTD at the hip, knee, and ankle were recorded. The RTD at 50-ms intervals up to 250 ms from force onset was calculated. The results of a stepwise multiple regression analysis, early RTD for hip flexion, and knee flexion were chosen as predictive variables for the maximum recoverable lean angle. The present study suggests that some of the early RTD in the lower limb muscles, but not the maximum isometric torque, can predict the maximum recoverable lean angle

Visual Feedback Position Tracking and Attitude Analysis of Two-Wheeled Vehicles Integrating a Target Vehicle Motion Model

This paper studies visual feedback position tracking control of two-wheeled vehicles in the situation that a camera and a target object are attached to the vehicles, respectively. Here, the body velocity of the target object vehicle is modeled as a Fourier series expansion. The relative position between the camera and the target object is controlled to the desired relative position. The present control law is based only on visual measurements, and the necessary information to implement the law is estimated from them. The asymptotic stability of the equilibrium of the total system including the internal attitude behavior is analyzed under some conditions of the target object vehicle velocity via stability theory of perturbed systems. Finally, a numerical simulation is conducted to show the effectiveness of the proposed method

Gaussian Control Barrier Functions : A Non-Parametric Paradigm to Safety

Inspired by the success of control barrier functions (CBFs) in addressing safety, and the rise of data-driven techniques for modeling functions, we propose a non-parametric approach for online synthesis of CBFs using Gaussian Processes (GPs). Mathematical constructs such as CBFs have achieved safety by designing a candidate function a priori. However, designing such a candidate function can be challenging. A practical example of such a setting would be to design a CBF in a disaster recovery scenario where safe and navigable regions need to be determined. The decision boundary for safety in such an example is unknown and cannot be designed a priori. In our approach, we work with safety samples or observations to construct the CBF online by assuming a flexible GP prior on these samples, and term our formulation as a Gaussian CBF. GPs have favorable properties, in addition to being non-parametric, such as analytical tractability and robust uncertainty estimation. This allows realizing the posterior components with high safety guarantees by incorporating variance estimation, while also computing associated partial derivatives in closed-form to achieve safe control. Moreover, the synthesized safety function from our approach allows changing the corresponding safe set arbitrarily based on the data, thus allowing non-convex safe sets. We validate our approach experimentally on a quadrotor by demonstrating safe control for fixed but arbitrary safe sets and collision avoidance where the safe set is constructed online. Finally, we juxtapose Gaussian CBFs with regular CBFs in the presence of noisy states to highlight its flexibility and robustness to noise. The experiment video can be seen at: https://youtu.be/HX6uokvCiGk

Robust pose tracking control for a fully-actuated hexarotor UAV based on Gaussian processes

This paper presents a robust position/attitude tracking control method for a fully-actuated hexarotor unmanned aerial vehicle (UAV) based on Gaussian processes. Multirotor UAVs suffer from modelling errors due to their structure complexity and aerodynamical disturbances whose perfect mathematical formulation is intractable. To handle this issue, this paper incorporates a data-based learning technique with model-based control. The hexarotor UAV dynamical model, considering modelling errors and aerodynamic disturbances as unknown dynamics, is first derived. Gaussian process regression is next introduced as a learning method for the unknown dynamics, which provides probabilistic distributions of the predicted values. The predicted means are regarded as deterministic information and cancelled out by feedforward control inputs. The predicted variances are considered as the bounds of the model uncertainties with high probability, and a robust control method to ensure ultimate boundedness of the tracking control error is proposed for the uncertain system. The effectiveness of the proposed method is demonstrated via experiments with a self-developed hexarotor UAV testbed