Optimal Control Based Path Planning for Parallel Kinematic Manipulators Utilising Natural Motion

Mirz, Christian; Schöler, Frederic; Barreto, Juan Pablo; Corves, Burkhard

doi:10.1109/coase.2018.8560547

Cited by 7 publications

(5 citation statements)

References 16 publications

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“…The serial configuration (adopted for example in References [42,50,79]) provides the actuator with a compliance that can be employed to decrease contact shocks and to reduce force peaks due to impacts, for example, In human-robot interaction [46]. On the other hand, the parallel configuration [65,[80][81][82] results in simpler mechanism and mathematics formulation [78]. Parallel compliance does not enlarge the configuration space of the robotic system and has a well-posed quadratic cost function for energy consumption minimization with respect to the compliance coefficients [83].…”

Section: Discussion Of Elastic Elements Configurationsmentioning

confidence: 99%

“…The majority of the works discussed in Section 2 neglect such an aspect and only consider point-to-point trajectories. Multi-point trajectories are taken into account in References [16,80,82,91,93,96]. Among these, H. Goya et al [16] and C. Mirz et al [82] use spring parameters that are optimized for the center of the interested areas to move the system following a multi-point trajectory.…”

Section: Discussionmentioning

confidence: 99%

“…Multi-point trajectories are taken into account in References [16,80,82,91,93,96]. Among these, H. Goya et al [16] and C. Mirz et al [82] use spring parameters that are optimized for the center of the interested areas to move the system following a multi-point trajectory. M. Shushtari et al [96] also consider one constant stiffness, whose value results from an optimization problem that takes into account the whole multi-point trajectory.…”

Section: Discussionmentioning

confidence: 99%

“…The optimal control theory is exploited by C. Mirz et al [82] to reduce energy consumption in parallel kinematic manipulators by means of linear torsional springs mounted in parallel to the motors. The power consumption of the drives is selected as cost function to calculate the optimal trajectory to travel between given initial and final positions in a fixed cycle time with minimum energy.…”

Section: Methods Based On the Optimal Control Theorymentioning

confidence: 99%

“…An alternative approach is to tackle the problem with an optimal control theory approach. This is used for the optimal design problems by M. Iwamura et al [56,100], by C. Mirz et al [82], who along with W. Scheilen et al [101] implement the Pontryagin's minimum principle (see Section 3.2.1).…”

Section: Design Optimization With Natural Motionmentioning

confidence: 99%

See 4 more Smart Citations

Natural Motion for Energy Saving in Robotic and Mechatronic Systems

et al. 2019

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Energy saving in robotic and mechatronic systems is becoming an evermore important topic in both industry and academia. One strategy to reduce the energy consumption, especially for cyclic tasks, is exploiting natural motion. We define natural motion as the system response caused by the conversion of potential elastic energy into kinetic energy. This motion can be both a forced response assisted by a motor or a free response. The application of the natural motion concepts allows for energy saving in tasks characterized by repetitive or cyclic motion. This review paper proposes a classification of several approaches to natural motion, starting from the compliant elements and the actuators needed for its implementation. Then several approaches to natural motion are discussed based on the trajectory followed by the system, providing useful information to the researchers dealing with natural motion.

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Section: Discussion Of Elastic Elements Configurationsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Methods Based On the Optimal Control Theorymentioning

confidence: 99%

Section: Design Optimization With Natural Motionmentioning

confidence: 99%

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Natural Motion for Energy Saving in Robotic and Mechatronic Systems

et al. 2019

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Optimal controller applied to robotic systems using covariant control equations

Rojas-Quintero

Rojas-Estrada

Villalobos-Chin

et al. 2021

International Journal of Control

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Optimal Control of Robotic Systems Using Finite Elements for Time Integration of Covariant Control Equations

2021

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We used an optimal control method involving covariant control equations as optimality conditions, to command the actuators of robot manipulators. These form a coupled system of second order nonlinear ordinary differential equations when associated with the robot motion equations. By solving this system, the control action required to take the robot from an initial to a final state is optimized in a prescribed time. However, the target set of equations exhibited stiffness. Therefore, an adequate solution could only be found for short trajectory durations with readily available numerical methods. We examined a time discretization procedure based on cubic and quintic Hermite finite elements which exhibited superconvergence properties for interpolation. This motivated us to develop a time integration algorithm based on Hermite's technique, where motion and control equations were perturbed to solve the optimal control problem. The optimal motion of a robotic manipulator was simulated using this algorithm. Our method was compared with a commercial differential equations solver on the basis of specific indicators. It outperformed the commercial solver by effectively solving the stiff set of equations for longer trajectory durations, with the cubic elements performing better than the quintic ones in this sense. The convergence analysis of our method confirmed that the quintic elements are more precise at the cost of increased computational burden, but converge at a lower rate than expected. Controlled motion experiments on a robotic manipulator validated our methodology. Trajectories were smoothly tracked and results exposed further methodology improvements.

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Optimal Control Based Path Planning for Parallel Kinematic Manipulators Utilising Natural Motion

Cited by 7 publications

References 16 publications

Natural Motion for Energy Saving in Robotic and Mechatronic Systems

Natural Motion for Energy Saving in Robotic and Mechatronic Systems

Optimal controller applied to robotic systems using covariant control equations

Optimal Control of Robotic Systems Using Finite Elements for Time Integration of Covariant Control Equations

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