Robust explicit model predictive control for hybrid linear systems with parameter uncertainties

Explicit model-predictive control (MPC) is a widely used control design method that employs optimization tools to find control policies offline; commonly it is posed as a semi-definite program (SDP) or as a mixed-integer SDP in the case of hybrid systems. However, mixed-integer SDPs are computationally expensive, motivating alternative formulations, such as zonotope-based MPC (zonotopes are a special type of symmetric polytopes). In this paper, we propose a robust explicit MPC method applicable to hybrid systems. More precisely, we extend existing zonotope-based MPC methods to account for multiplicative parametric uncertainty. Additionally, we propose a convex zonotope order reduction method that takes advantage of the iterative structure of the zonotope propagation problem to promote diagonal blocks in the zonotope generators and lower the number of decision variables. Finally, we developed a quasi-time-free policy choice algorithm, allowing the system to start from any point on the trajectory and avoid chattering associated with discrete switching of linear control policies based on the current state's membership in state-space regions. Last but not least, we verify the validity of the proposed methods on two experimental setups, varying physical parameters between experiments.

Residual Dynamics Learning for Trajectory Tracking for Multi-rotor Aerial Vehicles

This paper presents a technique to cope with the gap between high-level planning, e.g., reference trajectory tracking, and low-level controlling using a learning-based method in the plan-based control paradigm. The technique improves the smoothness of maneuvering through cluttered environments, especially targeting low-speed velocity profiles. In such a profile, external aerodynamic effects that are applied on the quadrotor can be neglected. Hence, we used a simplified motion model to represent the motion of the quadrotor when formulating the Nonlinear Model Predictive Control (NMPC)-based local planner. However, the simplified motion model causes residual dynamics between the high-level planner and the low-level controller. The Sparse Gaussian Process Regression-based technique is proposed to reduce these residual dynamics. The proposed technique is compared with Data-Driven MPC. The comparison results yield that an augmented residual dynamics model-based planner helps to reduce the nominal model error by a factor of 2 on average. Further, we compared the proposed complete framework with four other approaches. The proposed approach outperformed the others in terms of tracking the reference trajectory without colliding with obstacles with less flight time without losing computational efficiency.

Optimization-based Motion Planning for Multirotor Aerial Vehicles: a Review

In general, optimal motion planning can be performed both as local and as global. In such a planning, the choice in favor of either local or global planning technique mainly depends on whether the environmental conditions are dynamic or static. Hence, the most adequate choice is to use local planning or local planning alongside global planning. When designing optimal motion planning both as local or as global, the key metrics to bear in mind are execution time, asymptotic optimality, quick reaction on dynamic obstacles. Such planning approaches can address the aforesaid target metrics more efficiently compared to other approaches such as path planning followed by smoothing. Thus, the foremost objective of this study is to analyse related literature in order to understand how the motion planning, specially trajectory planning, problem is formulated, when being applied for generating optimal trajectories in real-time for Multirotor Aerial Vehicles (MAVs), impact the listed metrics. As result of the research, trajectory planning problem was broken down into a set of subproblems, the lists of methods for addressing each of the problems were identified and described in detail. Subsequently, the most prominent results from 2010 to 2022 were summarized and presented in the form of a timeline.

Non-linear stiffness behavior of planar serial robotic manipulators

The paper focuses on the stiffness analysis of multi-link serial planar manipulators, which may demonstrate nonlinear stiffness behavior under the compressive loading. Two important cases are considered, where the manipulator has either a straight or non-straight initial configuration. It was proved that in the first case the loading may cause the buckling if it exceeds some critical value, and the manipulator suddenly changes its straight shape and stiffness properties. For computing this critical force, a general eigenvalue-based technique was proposed that can be applied to any multi-link serial manipulator. For the second case dealing with non-straight initial configurations, a universal energy-based technique was applied that allowed to detect quasi-buckling phenomenon when it is observed very fast but not instant change of the manipulator shape and its stiffness coefficient under the loading. These results are illustrated by numerous examples of non-linear stiffness behavior of three-and four-link manipulators that are subjected to compressive force.

Optimization-based Trajectory Tracking Approach for Multi-rotor Aerial Vehicles in Unknown Environments

The goal of this paper is to develop a continuous optimization-based refinement of the reference trajectory to 'push it out' of the obstacle-occupied space in the global phase for Multi-rotor Aerial Vehicles in unknown environments. Our proposed approach comprises two planners: a global planner and a local planner. The global planner refines the initial reference trajectory when the trajectory goes either through an obstacle or near an obstacle and lets the local planner calculate a near-optimal control policy. The global planner comprises two convex programming approaches: the first one helps to refine the reference trajectory, and the second one helps to recover the reference trajectory if the first approach fails to refine. The global planner mainly focuses on real-time performance and obstacles avoidance, whereas the proposed formulation of the constrained nonlinear model predictive control-based local planner ensures safety, dynamic feasibility, and the reference trajectory tracking accuracy for low-speed maneuvers, provided that local and global planners have mean computation times 0.06s (15Hz) and 0.05s (20Hz), respectively, on an NVIDIA Jetson Xavier NX computer. The results of our experiment confirmed that, in cluttered environments, the proposed approach outperformed three other approaches: sampling-based pathfinding followed by trajectory generation, a local planner, and graph-based pathfinding followed by trajectory generation.

Kinematic Control of compliant serial manipulators composed of dual-triangles

The paper focuses on the kinematics control of a compliant serial manipulator composed of a new type of dualtriangle elastic segments. Some useful optimization techniques were applied to solve the geometric redundancy problem, ensure the stability of the manipulator configurations with respect to the external forces/torques applied to the endeffector. The efficiency of the developed control algorisms is confirmed by simulation.

Mechanics of compliant serial manipulator composed of dual-triangle segments

The paper focuses on the mechanics of a compliant serial manipulator composed of new type of dual-triangle elastic segments. Both the analytical and numerical methods were used to find the manipulator stable and unstable equilibrium configurations, as well as to predict corresponding manipulator shapes. The stiffness analysis was carried on for both loaded and unloaded modes, the stiffness matrices were computed using the Virtual Joint Method (VJM). The results demonstrate that either buckling or quasi-buckling phenomenon may occur under the loading, if the manipulator corresponding initial configuration is straight or non-straight one. Relevant simulation results are presented that confirm the theoretical study.

Path Planning Followed by Kinodynamic Smoothing for Multirotor Aerial Vehicles (MAVs)

We explore path planning followed by kinodynamic smoothing while ensuring the vehicle dynamics feasibility for MAVs. We have chosen a geometrically based motion planning technique \textquotedblleft RRT*\textquotedblright\; for this purpose. In the proposed technique, we modified original RRT* introducing an adaptive search space and a steering function which help to increase the consistency of the planner. Moreover, we propose multiple RRT* which generates a set of desired paths, provided that the optimal path is selected among them. Then, apply kinodynamic smoothing, which will result in dynamically feasible as well as obstacle-free path. Thereafter, a b spline-based trajectory is generated to maneuver vehicle autonomously in unknown environments. Finally, we have tested the proposed technique in various simulated environments.

Real-Time Long Range Trajectory Replanning for UAVs in Presence of Dynamics Obstacles

Real-time long-range local planning is a challenging task, especially in the presence of dynamics obstacles. We propose a complete system which is capable of performing the local replanning in real-time. It requires to provide the desired trajectory to be followed in the system initialization phase. Subsequently, it starts initializing sub-components of the system including point cloud processor, trajectory estimator and planner. Afterwards, the multi-rotary aerial vehicle starts moving on the given trajectory. When it detects obstacles, it replans the trajectory from the current pose to pre-defined distance incorporating the desired trajectory. Point cloud processor is employed to identify the closest obstacles around the vehicle. For replanning, Rapidly-exploring Random Trees (RRT*) is used with two modifications which allow planning the trajectory in milliseconds scales. Once we replanned trajectory, velocity components(x,y and z) and yaw rate are calculated. Those values are sent to the controller at a constant frequency to navigate the vehicle autonomously. Finally, we have evaluated each of the components separately and tested the complete system in the simulated and real environment.

Ground and Non-Ground Separation Filter for UAV Lidar Point Cloud

This paper proposes a novel approach for separating ground plane and non-ground objects on Lidar 3D point cloud as a filter. It is specially designed for real-time applications on unmanned aerial vehicles and works on sparse Lidar point clouds without preliminary mapping. We use this filter as a crucial component of fast obstacle avoidance system for agriculture drone operating at low altitude. As the first step, a point cloud is transformed into a depth image and then places with high density nearest to the vehicle (local maxima) are identified. Then we merge original depth image with identified locations after maximizing intensities of pixels in which local maxima were found. Next step is to calculate range angle image which represents angles between two consecutive laser beams based on improved depth image. Once a range angle image is constructed, smoothing is applied to reduce the noise. Finally, we find out connected components in the improved depth image while incorporating smoothed range angle image. This allows separating the non-ground objects. The rest of the locations of depth image belong to the ground plane. The filter has been tested on a simulated environment as well as an actual drone and provides real-time performance. We make our source code and dataset available online\footnote[2]{Source code and dataset are available at https://github.com/GPrathap/hagen.git