Time-optimal Robot Research Articles

Near-time optimal feedrate planning for the NURBS curve considering interpolation error constraints

Compared with general time-optimal robot feedrate planning, trajectory machining tasks require consideration of feedrate command constraints and the complexity of parameter spline curves. The interpolation error generated during the interpolation stage affects the command accuracy and contour accuracy of the trajectory. To ensure that the robot end-effector feedrate maintains consistency with the feedrate command and to improve the contour accuracy of the trajectory, this study proposes a two-stage method: near-time optimal feedrate planning for the NURBS curve considering interpolation error constraints. In the first stage, the end-effector velocity constraint under joint velocity constraint is calculated, and the feedrate command is corrected based on that constraint. Then, the corrected feedrate command is transformed into parameter form, and feedrate planning is carried out utilizing the direct transcription method. In the second stage, interpolation is carried out after feedrate planning, and interpolation error is calculated to detect any over-limit positions. If any over-limit positions are detected, the first over-limit position is recorded, and feedrate planning with reduced feedrate limit is carried out at that position. This process is repeated until the interpolation error constraint is satisfied. A series of simulations and experiments were conducted in this study. The simulation results show that the proposed method can consider feedrate command constraints and limit interpolation errors within specified constraints. The experimental results show that the proposed method can reduce contour errors, particularly at low feedrate command.

A Spatio-Temporal Prediction and Planning Framework for Proactive Human–Robot Collaboration

AbstractA significant challenge in human–robot collaboration (HRC) is coordinating robot and human motions. Discoordination can lead to production delays and human discomfort. Prior works seek coordination by planning robot paths that consider humans or their anticipated occupancy as static obstacles, making them nearsighted and prone to entrapment by human motion. This work presents the spatio-temporal avoidance of predictions-prediction and planning framework (STAP-PPF) to improve robot–human coordination in HRC. STAP-PPF predicts multi-step human motion sequences based on the locations of objects the human manipulates. STAP-PPF then proactively determines time-optimal robot paths considering predicted human motion and robot speed restrictions anticipated according to the ISO15066 speed and separation monitoring (SSM) mode. When executing robot paths, STAP-PPF continuously updates human motion predictions. In real-time, STAP-PPF warps the robot’s path to account for continuously updated human motion predictions and updated SSM effects to mitigate delays and human discomfort. Results show the STAP-PPF generates robot trajectories of shorter duration. STAP-PPF robot trajectories also adapted better to real-time human motion deviation. STAP-PPF robot trajectories also maintain greater robot/human separation throughout tasks requiring close human–robot interaction. Tests with an assembly sequence demonstrate STAP-PPF’s ability to predict multi-step human tasks and plan robot motions for the sequence. STAP-PPF also most accurately estimates robot trajectory durations, within 30% of actual, which can be used to adapt the robot sequencing to minimize disruption.

A finite and fast time-optimal trajectory planning based on velocity sinking method for robots along specified path

Time-optimal trajectory planning is used in many areas of industrial robots and has a wide range of applications. This paper presents a finite and fast computation method for calculating time-optimal robot trajectories along specified geometric paths, namely the velocity sinking method. The velocity sinking method differs from those proposed in the existing literature which solve uncertain optimization problem. Firstly, the maximum velocity in multiple state constraints is calculated using a path parameterization method. Then, the pseudo maximum velocity trajectory is calculated using a numerical integration method. Finally, the time-optimal trajectory planning under path constraints is determined using an iterative velocity sinking algorithm. The experiment demonstrates the effectiveness and efficiency of this method in industrial robotic settings.

Time-optimal robotic manipulation on a predefined path of loosely placed objects: Modeling and experiment

A consistent method is presented for solving the so-called general waiter problem, which is to move a tray (mounted at the end-effector of a robot) with a number of loosely placed objects (e.g. cups) as fast as possible such that the objects do not slide at any time. The geometric path of the tray motion is prescribed while the attitude of the tray must vary in order to avoid sliding or tip-over of the objects. The time optimal robot trajectory is determined with a multiple shooting method. For the considered wrist-partitioned robot, the motion is described by the path parameter and the three joint coordinates of the wrist. This 4-parametric description is beneficial for solving the optimal control problem with improved convergence. The optimization takes into account the technical limitations of the robot as well as the limiting friction between objects and tray. Experimental results for a time-optimal motion of a Stäubli RX130L manipulating a tray with 4 cups are presented. A crucial aspect is the use of a model-based control strategy along with the identification of dynamic parameters. Moreover, the basis for any optimization and real-time control is a reliable dynamic model of the robot. Therefore a parameter identification is performed using optimized persistent excitation trajectories.

Single landmark feedback-based time optimal navigation for a differential drive robot

In this paper, we propose a feedback-based control approach to execute the time optimal motion trajectories for a differential drive robot. These trajectories are composed of straight lines and rotations in place. We show that the evolution of the position of a single landmark over time, in a local reference frame, makes it possible to track a prescribed time-optimal robot’s trajectory, based on feedback of the landmark’s position. We also show that the closed-loop system is an exponentially stable one with a nonvanishing perturbation, and that globally uniformly ultimately boundedness of the tracking errors can be achieved. The two main results of this work are: 1) Our approach leverages visual servo control type of methods with tools from optimal control for executing time-optimal trajectories in the state space based on feedback information. 2) The approach is able to work with the minimum number of landmarks–only one–this represents a necessary and sufficientcondition for landmark-based navigation. Experiments in a physical robot, a nonholonomic differential drive system equipped with an omnidirectional laser sensor, are shown, which validate the proposed theoretical modelling.

Time-optimal tool motion planning with tool-tip kinematic constraints for robotic machining of sculptured surfaces

Abstract A time-optimal motion planning method for robotic machining of sculptured surfaces is reported in this paper. Compared with the general time-optimal robot motion planning, a surface machining process provides extra constraints such as tool-tip kinematic limits and complexity of the curved tool path that also need to be taken into account. In the proposed method, joint space and tool-tip kinematic constraints are considered. As there are high requirements for tool path following accuracy, an efficient numerical integration method based on the Pontryagin maximum principle is adopted as the solver for the time-optimal tool motion planning problem in robotic machining. Nonetheless, coupled and multi-dimensional constraints make it difficult to solve the problem by numerical integration directly. Therefore, a new method is provided to simplify the constraints in this work. The algorithm is implemented on the ROS (robot operating system) platform. The geometry tool path is generated by the CAM software firstly. And then the whole machine moving process, i.e. the feedrate of machining process, is scheduled by the proposed method. As a case study, a sculptured surface is machined by the developed method with a 6-DOF robot driven by the ROS controller. The experimental results validate the developed algorithm and reveal its advantages over other conventional motion planning algorithms for robotic machining.

Successive dynamic programming and subsequent spline optimization for smooth time optimal robot path tracking

Abstract. The time optimal path tracking for industrial robots regards the problem of generating trajectories that follow predefined end-effector (EE) paths in shortest time possible taking into account kinematic and dynamic constraints. The complicated tasks used in industrial applications lead to very long EE paths. At the same time smooth trajectories are mandatory in order to increase the service life. The consideration of jerk and torque rate restrictions, necessary to achieve smooth trajectories, causes enormous numerical effort, and increases computation times. This is in particular due to the high number of optimization variables required for long geometric paths. In this paper we propose an approach where the path is split into segments. For each individual segment a smooth time optimal trajectory is determined and represented by a spline. The overall trajectory is then found by assembling these splines to the solution for the whole path. Further we will show that by using splines, the jerks are automatically bounded so that the jerk constraints do not have to be imposed in the optimization, which reduces the computational complexity. We present experimental results for a six-axis industrial robot. The proposed approach provides smooth time optimal trajectories for arbitrary long geometric paths in an efficient way.

Convex time-optimal robot path following with Cartesian acceleration and inertial force and torque constraints

In time-optimal robot path following, a predetermined geometric trajectory is followed exactly in a time-optimal way considering system constraints, for example, actuator constraints. For a simplified robotic manipulator, this optimization problem can be reformulated into a convex optimization problem when only considering some system constraints. In this article, the convex approach is extended to account for Cartesian acceleration constraints and in turn account for inertial forces and torques acting on a load held by the robot. The focus of this article is on the reformulation of these Cartesian acceleration and inertial forces and torques to preserve the convexity of the optimization problem. We present a series of applications that result in solving a convex optimization problem, illustrating the practicality of the proposed reformulations.

Optimal Motion Planning of Spot Welding Robot Applications

This paper discusses the problem of effective motion planning for industrial robots. The first part dealt with current method for off-line motion planning. In the second part the presented work is done by one of the simulation systems with automatic trajectory generation and off-line programming capability. A spot welding process is involved. The practical application of this step strongly depends on the method for robot path optimization with high accuracy, thus transform the path into a time and energy optimal robot program for the real world, which is discussed in the third step.

Path Planning with Motion Optimization for Car Body-in-White Industrial Robot Applications

This paper discusses the problem of effective motion planning for industrial robots. The first part dealt with current method for off-line motion planning. In the second part the presented work is done by one of the simulation systems with automatic trajectory generation and off-line programming capability. A spot welding process is involved. The practical application of this step strongly depends on the method for robot path optimization with high accuracy, thus transform the path into a time and energy optimal robot program for the real world, which is discussed in the third step.

Mechanical assessment of time optimal robot motion

The use of time optimal path planning can speed up robots on assembly lines and allow them to run faster, increasing their productivity. This paper seeks to develop a more complete understanding of the nature of time-optimal point-to-point trajectories for polar coordinate robots and intends to show how effective direct numerical methods are in computing optimal control solutions, including the resolution of complicated motor switching structures. In time optimal robot point-to-point motion there is generically one robot axis that has the hardest time reaching its endpoint. And then, to whatever extent other axes have extra freedom, it must be used to help the axis with the hardest task, whenever possible. Such assistance makes use of different mechanical interaction forces and effects. In this paper we examine one basis type of robot, the polar coordinate robot, and analyze all types of forces during optimal motions, in order to develop an understanding of optimal maneuvers.

Synthesis of topology and sizing of analog electrical circuits by means of genetic programming

The design (synthesis) of an analog electrical circuit entails the creation of both the topology and sizing (numerical values) of all of the circuit's components. There has previously been no general automated technique for automatically creating the design for an analog electrical circuit from a high-level statement of the circuit's desired behavior. This paper shows how genetic programming can be used to automate the design of eight prototypical analog circuits, including a lowpass filter, a highpass filter, a bandstop filter, a tri-state frequency discriminator circuit, a frequency-measuring circuit, a 60 dB amplifier, a computational circuit for the square root function, and a time-optimal robot controller circuit.

Dynamic Load Carrying Capacity of Mechanical Manipulators—Part II: Computational Procedure and Applications

A computational procedure is presented for obtaining numerical solutions to the trajectory optimization problem associated with synthesizing robot dynamic trajectories with maximum load carrying capacities. The applications of the procedure and the problem formulations given in Part I of this paper to synthesizing time-optimal robot motions and classification of multi-degree-of-freedom robot manipulators are also investigated.