IMBiO3R - Trajectory_control

A new linear algebra model-based controller for a 4dof parallel robot

avalera — Tue, 07 Jun 2022 18:11:31 +0000

This paper presents a new controller for parallel robots. The design of the controller is based on the dynamic robot model, and it uses Linear Algebra Theory and Numerical Methods. The controller stability analysis demonstrates that it is globally uniformly asymptotically stable. Simulations and experimental results with an actual 3UPS+RPU parallel robot confirm the feasibility and the effectiveness of the proposed controller. The new strategy allows an intuitive adjustment of parameters, the computational cost is low, and the robot is able to follow the trajectory references closely.

Trajectory_control

Compliant admittance-coupled DMP with Type II singularity evader

avalera — Tue, 07 Jun 2022 18:10:18 +0000

This video shows the execution of a trajectory generated by Dynamic Movement Primitives (DMP) to simultaneously provide an admittance behavior and avoid Type II singular configurations for the 4-DOF parallel robot. The trajectory is modified by one coupling action defined for the human-robot admittance interaction and another for the singularity avoidance.

The original reference trajectory is static and initially close to a singularity in the axis of rotation around Z (ψ). In this experiment, the human tries to push the robot toward the singularity by exerting a torque on Z (bottom-right chart), which provokes its rotation thanks to the admittance behavior (bottom-left chart). However, as soon as the minΩ_c singularity indicator falls below the limit, the evader is activated through a coupling action and keeps the robot out of the singularity, also ceasing the admittance behavior gradually. This results in a struggle between the human and the robot with smooth movements to ensure their safety. In the charts, “ref” is the reference of the rotation around Z, “meas” is the measurement of the signals, and “lim” is the limit for minΩ_c.

The core controller is a PD+G, used to track the trajectory generated by the DMP, affected by both coupling actions.

Trajectory_control

Admittance control with Type II Singularity evader

avalera — Tue, 07 Jun 2022 16:43:56 +0000

A compliant-admittance controller complemented with a Type II evader module is implemented on a 4-DOF parallel robot. The Type II singularity evader provides complete user control over the robot because the evader modifies online the actuators’ trajectory if a singularity is close. The proximity to a singularity is measured by the minimum angle Ω. The location of the actuator on limb 3 is presented to verify the activation of the evader module, while the robot's location on z_m measured by a 3D tracking system demonstrates the complete control over the robot. In the figures, the subindex “a” represents the admittance reference, the subindex “d” stands for evader modifications, the subindex “c” stands for measurements, and the “lim” represents the experimental limits.

Trajectory_control

Admittance control without Type II Singularity evader

avalera — Tue, 07 Jun 2022 15:25:52 +0000

A raw compliant-admittance controller implemented on a 4-DOF parallel robot. The video shows how the user drives the robot to a Type II singularity and loses control with a final fall of the robot. The proximity to a singularity is measured by the determinant of the forward Jacobian (‖J_D ‖) and the minimum angle Ω. The robot's location on z_m, measured by a 3D tracking system, verifies the robot's fall. In the figures, the subindex “a” represents the admittance reference, the subindex “c” stands for measurements, and the “lim” represents the experimental limits.

Trajectory_control

Admittance control with Type II Singularity evader testing with a humans knee

avalera — Tue, 07 Jun 2022 15:22:53 +0000

A compliant-admittance controller complemented with a Type II evader module is implemented on a 4-DOF parallel robot and tested with a patient. The Type II singularity evader provides complete user control over the robot because the evader modifies online the actuators’ trajectory if a singularity is close. The proximity to a singularity is measured by the minimum angle Ω. The location of the actuator corresponding to limb 3 is presented to verify the activation of the evader module, while the moment around the z_m axis, measured by a force sensor, demonstrates the non-dangerous effort performed by the patient. In the figures, the subindex “a” represents the admittance reference, the subindex “d” stands for evader modifications, the subindex “c” stands for measurements, and the “lim” represents the experimental limits.

Trajectory_control

Compliant admittance-coupled DMP without Type II singularity evader

avalera — Sun, 05 Jun 2022 16:24:01 +0000

This video shows the execution of a trajectory generated by Dynamic Movement Primitives (DMP) to provide an admittance behavior for the 4-DOF parallel robot. A coupling action is defined as the difference between a reference force and the exerted force, and this coupling action is fed to the DMP to allow the compliant manipulation.

The original reference trajectory is static in position and zero in force, so any external force triggers the movement of the mobile platform. However, in this video, the authors want to emphasize the problem of this kind of scheme in parallel robots: the control of the human upon the robot because of the compliant manipulation may lead the robot to a singular configuration and a subsequent control loss. Indeed, the original trajectory is close to a singularity in the axis of rotation around Z (ψ), so a moment on this axis (bottom-right chart) may cause its movement (bottom-left chart) to enter a singular configuration (which is measured by minΩ_c in the top chart), and the robot eventually responds unpredictably. The solution for this is the incorporation of a Type II singularity evader. In the charts, “ref” is the reference of the rotation around Z, “meas” is the measurement of the signals, and “lim” is the limit for minΩ_c.

The core controller is a PD+G, used to track the trajectory generated by the DMP.

Trajectory_control

Type II singularity evader effect on a singular trajectory encoded with DMP

avalera — Sat, 04 Jun 2022 15:00:04 +0000

This video shows the execution of a trajectory generated by Dynamic Movement Primitives (DMP) to avoid Type II singular configurations for the 4-DOF parallel robot. To this end, an initial singular trajectory is encoded by the DMP, which is modified during execution by using coupling actions.

Those coupling actions are activated when either the determinant of the forward Jacobian ||J_D || or the minimum angle between two OTS minΩ_c fall below a threshold. Their values are obtained using a vision system to measure the cartesian pose, and only the two limbs most responsible for the singularity are affected by the coupling action. In this experiment, limbs 3 and 4 are deviated from their original reference (bottom charts) to keep the minΩ_c in the limit (top chart). In the charts, “ref” is the reference of the joint positions, “meas” is the measurement of the signals, and “lim” is the limit for minΩ_c.

A core PD+G controller tracks the modified trajectory free of singularities. The coupling actions are defined through objective controls on the variables ||J_D || and minΩ_c.

Trajectory_control

Hybrid control: identification of two parameters (high-speed, high-resolution video summary)

avalera — Tue, 01 Jun 2021 16:21:04 +0000

Hybrid control: identification of two parameters (high-speed, high-resolution video summary)

This video shows the execution of a new controller for the 4dof parallel robot. It is a hybrid controller that uses window-based least (WLS)
squares or recursive least squares (RLS) for the identification of the robot’s parameters. In this case, by means RLS we estimate the first
and second relevant parameters. The first relevant parameter corresponds basically to the mobile platform mass and the second relevant parameter
represent the first inertia moment on X axis of the limb 1.

In order to verify the developed controller, some experiments have been carried out. For these experiments, the trajectories employed involve
sinusoidal movements around the generalized coordinates (x, z, θ, ψ), wich sntail two hip flexion combined with flexion-extension of knee.
Four pauses are introduced where the robot maintains the mobile platform horizontally in a fixed position, waiting for a payload to be placed
(or removed) during 20 seconds. Starting with no payload (stage 1), a 25 kg payload is placed at instant t=100 s (stage 2) and moved away
at t=220 s (stage 3). Afterwards, a 15 kg payload is placed at t=340 s (stage 4) and removed at instant t=460 s (stage 5).

Trajectory_control

Hybrid control: identification of one parameter (high-speed, high-resolution video summary)

avalera — Tue, 01 Jun 2021 15:55:20 +0000

Hybrid control: identification of one parameter (high-speed, high-resolution video summary)

This video shows the execution of a new controller for the 4dof parallel robot. It is a hybrid controller that uses window-based least (WLS)
squares or recursive least squares (RLS) for the identification of the robot’s parameters. In this case, by means RLS we estimate the first
relevant parameter that basically corresponds with the mobile platform mass.

Trajectory_control

Hybrid control: identification of one parameter

avalera — Mon, 01 Mar 2021 11:09:26 +0000

This video shows the execution of a new controller for the 4dof parallel robot. It is a hybrid controller that uses window-based least (WLS) squares or recursive least squares (RLS) for the identification of the robot’s parameters. In this case, by means RLS we estimate the first relevant parameter that basically corresponds with the mobile platform mass.

In order to verify the developed controller, some experiments have been carried out. For these experiments, the trajectories employed involve sinusoidal movements around the generalized coordinates (x, z, θ, ψ), wich sntail two hip flexion combined with flexion-extension of knee. Four pauses are introduced where the robot maintains the mobile platform horizontally in a fixed position, waiting for a payload to be placed (or removed) during 20 seconds. Starting with no payload (stage 1), a 25 kg payload is placed at instant t=100 s (stage 2) and moved away at t=220 s (stage 3). Afterwards, a 15 kg payload is placed at t=340 s (stage 4) and removed at instant t=460 s (stage 5).

Trajectory_control