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Given starting and ending positions and velocities, L2 bounds on the acceleration and velocity, and the restriction to no more than two constant control inputs, this paper provides routines to compute the minimal-time path. Closed form solutions are provided for reaching a position in minimum time with and without a velocity bound, and for stopping at the goal position. A numeric solver is used to reach a goal position and velocity with no more than two constant control inputs. If a cruising phase at the terminal velocity is needed, this requires solving a non-linear equation with a single parameter. Code is provided on GitHub 1 , extended paper version at [1]. [1] https://github.com/RoboticSwarmControl/MinTimeL2pathsConstraints/ 

This work presents an online trajectory generation algorithm using a sinusoidal jerk profile. The generator takes initial acceleration, velocity and position as input, and plans a multi-segment trajectory to a goal position under jerk, acceleration, and velocity limits. By analyzing the critical constraints and conditions, the corresponding closed-form solution for the time factors and trajectory profiles are derived. The proposed algorithm was first derived in Mathematica and then converted into a C++ implementation. Finally, the algorithm was utilized and demonstrated in ROS & Gazebo using a UR3 robot. Both the Mathematica and C++ implementations can be accessed at https://github.com/Haoran-Zhao/Jerk-continuous-online-trajectory-generator-with-constraints.git 

This paper presents four data-driven system models for a magnetically controlled swimmer. The models were derived directly from experimental data, and the accuracy of the models was experimentally demonstrated. Our previous study successfully implemented two non-model-based control algorithms for 3D path-following using PID and model reference adaptive controller (MRAC). This paper focuses on system identification using only experimental data and a model-based control strategy. Four system models were derived: (1) a physical estimation model, (2, 3) Sparse Identification of Nonlinear Dynamics (SINDY), linear system and nonlinear system, and (4) multilayer perceptron (MLP). All four system models were implemented as an estimator of a multi-step Kalman filter. The maximum required sensing interval was increased from 180 ms to 420 ms and the respective tracking error decreased from 9 mm to 4.6 mm. Finally, a Model Predictive Controller (MPC) implementing the linear SINDY model was tested for 3D path-following and shown to be computationally efficient and offers performances comparable to other control methods. 

Rotating miniature magnetic swimmers are de-vices that could navigate within the bloodstream to access remote locations of the body and perform minimally invasive procedures. The rotational movement could be used, for example, to abrade a pulmonary embolus. Some regions, such as the heart, are challenging to navigate. Cardiac and respiratory motions of the heart combined with a fast and variable blood flow necessitate a highly agile swimmer. This swimmer should minimize contact with the walls of the blood vessels and the cardiac structures to mitigate the risk of complications. This paper presents experimental tests of a millimeter-scale magnetic helical swimmer navigating in a blood-mimicking solution and describes its turning capabilities. The step-out frequency and the position error were measured for different values of turn radius. The paper also introduces rapid movements that increase the swimmer's agility and demonstrates these experimentally on a complex 3D trajectory. 

Consider many particles actuated by a uniform global external field (e.g. gravitational or magnetic fields). This paper presents analytical results using workspace obstacles and global inputs to reshape such a group of particles. Shape control of many particles is necessary for conveying information, construction, and navigation. First we show how the particles’ characteristic angle of repose can be used to reshape the particles by controlling angle of attack and the magnitude of the driving force. These can then be used to control the force and torque applied to a rectangular rigid body. Next, we examine the full set of stable, achievable mean and variance configurations for the shape of a particle group in two canonical environments: a square and a circular workspace. Finally, we show how workspaces with linear boundary layers can be used to achieve a more rich set of mean and variance configurations. 

This study investigates the high speed 3D navigation of rotating millimeter-scale swimmers. The swimmers have a spiral-shaped surface to ensure propulsion. The rotational movement is used for propulsion and, in future work, could provide the power needed to remove blood clots. For instance, an abrasive tip could be used to progressively grind a blood clot. An algorithm to perform 3D control of rotating millimeterscale swimmers was implemented and tested experimentally. The swimmers can follow a trajectory and can navigate without touching the walls inside a tube having a diameter of 15 mm. This diameter is smaller than the average diameter of the distal descending aorta, which is the smallest section of the aorta. Several swimmers designs were built and tested. The maximum velocity recorded for our best swimmer was 103.6 mm/s with a rotational speed of 477.5 rotations per second.