The increased complexity of vehicle testing can be attributed to the rapid development of technical advancements within the automotive industry, thereby prolonging the time to market of a product. The process of allocating and coordinating vehicle tests at proving grounds (PGs) is a complex and time-consuming task. Currently, this process is still performed manually, which is inefficient. This study proposes a methodology for assigning scenarios to designated sites, taking into account travel aspects between locations and fulfilling participant requirements. The allocation procedure is formulated as an Open Job Shop Scheduling problem with temporal synchronisation and skill matching, and is solved by the Constraint Programming tool Google OR-Tools. The efficacy of the approach is demonstrated by its ability to generate a close-to-optimal schedule to fulfil customer requests. Case studies demonstrate that a combination of two distinct objectives are essential to meet the demands of compactness and time efficiency. The findings of this study provide a solid foundation for enhancing automation at a PG, thereby improving efficiency and optimising testing processes.

Interpolation of rigid body motions, or a general frame motion in Euclidean space, is a recurring topic in robotics. It boils down to generating trajectories in a Lie group, either SE (3) or SO (3) × ℝ3, with given initial and/or terminal values. To this end, spline interpolation schemes were developed where canonical coordinates are represented by cubic splines. They allow for prescribing initial velocity and acceleration only. In many robotic applications, terminal conditions are prescribed, however. In this paper, a novel interpolation scheme is presented that admits prescribing the terminal pose, velocity and acceleration, or the initial condition. As example, the scheme is applied to a rendezvous task of a UAV and describing the deformation of a Cosserat beam as relevant for soft robotics. The presented interpolation scheme can be directly applied to the motion parameterization in terms of (dual) quaternions.

The kinematics of cuspidal 3R regional robots was studied extensively in the past. Moreover, certain industrial 6R robots were found to be cuspidal (e.g. Fanuc CRX series, Kinova GEN2), which makes cuspidal robots finally interesting for practical applications. This necessitates optimal trajectory planning, respecting the dynamics and technical limits of the particular robot. In this paper, a method for singularity-free time-optimal point-to-point trajectory (PtP) trajectory planning is proposed. As a special case, this method is applicable to time-optimal singularity-free assembly mode changing. Results are shown for 3R robots and a 6R Fanuc CRX10iA/L.

Parallel kinematics machines (PKM) operate with maximal acceleration being designed for highly dynamic manipulation tasks. This leads to extreme loads of the joints, which is usually not accounted for in the motion planning. In this paper an extended inverse dynamics method is introduced, which allows computing the joint reaction forces along with the actuation torques, and provides a basis for time optimal motion planning and control minimizing wear of the components. To this end, PKM are modeled using absolute coordinates. The joint constraints are complemented with servo constraints so that the motion can be described by the actuator motion or by the end-effector motion. The presented method is particularly advantageous when certain model parameters are unknown and allows for model simplification, which would not be possible for the relative coordinate formulation. The sparsity of the obtained velocity constraint Jacobian matrix, due to the use of absolute coordinates, can be efficiently exploited to minimize computation time. The method is demonstrated and numerical results are reported for a time-optimal pick and place movement of a 4-DOF Delta robot.

Quality assessment of products produced in small numbers requires discontinuous allocation of work forces. Automatizing these processes leads to a significant increase in cost efficiency. In this paper the testing of a mechatronic product is addressed, which requires in particular connecting it to a controller by means of an electric plug. The paper presents a robotic solution that allows to robustly accomplish the electric connection. The solution relies on a model-based hybrid force-position control of an industrial robot. The particular challenge is that the electric plug is multipolar, i.e. it must be inserted with a certain orientation. The latter necessitates a two stage approach for insertion, which distinguishes this problem from the classical peg-in-the-hole problem. Experimental results are presented for a prototype implementation on the real hardware. These results show a high success rate, and prove the practical applicability of the developed method.

This paper presents a new dynamic programming (DP) approach to the optimal path following problem. The method rests on an interpolation in the phase plane so that the resulting joint accelerations and joint torques are continuous. This allows for taking into account limits on the joint jerks and torque rates in addition to joint velocities, accelerations, torques, and the mechanical power. Most methods proposed in the literature yield values of optimal trajectories at discrete sampling times so that this must be interpolated subsequently to the trajectory optimization. This causes violations of the joint jerk and torque rate limits. The proposed method does not suffer from this problem, which is a main feature of this approach. Unlike most of the previously proposed methods, joint jerk and torque rate limits are addressed with a reasonable increase in the computation time of DP algorithms. Special attention is given to experimental validation of the optimization results. The presented experimental results confirm the importance of taking the motor torque characteristics as well as the Coulomb and viscous friction into account. Neglecting these effects (as most previous publications did) leads to trajectories that cannot be performed by real manipulators. Apart from DP, other approaches with smaller computation times exist. However, most of these methods are either limited to the time optimal case (which might not always be the desired criterion) and are not able to handle all earlier mentioned constraints or cannot take into account viscous friction effects. Apart from that a sequential convex programming (SCP) approach exists, which accounts for the same constraints as the presented approach. Therefore, the proposed DP approach is compared to this SCP method and an example is presented where the time optimal trajectory is performed by a real manipulator.

Time-optimal motion control will only find industrial applications if the optimal motions can actually be performed by standard industrial robots. This is not ensured by any optimal motion planning scheme proposed up to now. The limiting aspect rendering all these schemes impractical is the insufficient continuity of the motion trajectories. In this paper, a time-optimal path following along a predefined end-effector path is addressed for kinematically redundant robots, where nonredundant robots are included as special cases. As prerequisite explicit expressions for the higher order inverse kinematics are presented. Kinematic redundancy is resolved and exploited within the trajectory planning using the joint space decomposition and a novel pseudoinverse-based solution of the higher order inverse kinematics. The approaches are demonstrated for two examples of kinematically redundant manipulators performing time-optimal motions along prescribed end-effector paths in compliance with technological constraints. The optimization results are experimentally validated.

The classical optimal path following problem considers the problem of moving optimally along a predefined geometric path under technological restrictions. In contrast to optimal path following, optimal tube following allows deviations from the initial path within a predefined tube to reduce cost even more. The present paper proposes a modern approach that treats this non-convex problem in task space. This novel method also provides a simple way to derive optimal trajectories within a tube described in terms of polygonal lines. Numerical examples are presented that allow to compare the proposed method to existing joint space approaches.

Minimum-time trajectories for applications where a geometric path is followed by a kinematically redundant robot’s end-effector may yield economical improvements in many cases compared to conventional manipulators. While for non-redundant robots the problem of finding such trajectories has been solved, the redundant case has not been treated exhaustively. In this contribution, the problem is split into two interlaced parts: inverse kinematics and trajectory optimization. In a direct optimization approach, the inverse kinematics problem is solved numerically at each time point. Therein, the manupulator’s kinematic redundancy is exploited by introducing scaled nullspace basis vectors of the Jacobian of differential velocities. The scaling factors for each time point are decision variables, thus the inverse kinematics is solved optimally w.r.t. the trajectory optimization goal, i.e. minimizing end time. The effectiveness of the presented method is shown by means of the example of a planar 4R manipulator with two redundant degrees of freedom.

Vehicles with several centered orientable wheels have one of the highest maneuverability and are hence an excellent choice for transportation tasks in narrow environments. However, they are non-holonomic, in general redundantly actuated, and additionally suffer from configuration singularities, which makes their modeling and control challenging. Existing control approaches only consider the vehicle kinematics whereas the required torques are commonly controlled by classical PD motor controllers. However, this leads to considerable tracking errors and a violation of the constraints especially during acceleration phases. Moreover, actuator counteractions and an undefined torque distribution can be observed. This paper introduces a model-based control concept that overcomes these issues. It resolves counteractions and distributes torques according to physical limitations which significantly reduces slippage and the energy consumption and further reduces the tracking error. To this end, an inverse dynamics solution of a redundantly parametrized model is used. The method is robust to configuration singularities. This is confirmed by experimental results.

Nowadays robotic manipulators are used as multi-purpose tools and must be able to complete various tasks. Pure position control schemes are often not sufficient to fulfill the requirements of these tasks. Interaction with the environment requires an extension of the conventional position control in order to achieve a desired compliance, and thus to limit the impact in order to avoid damaging of involved objects. This paper presents an admittance control scheme applicable to kinematically redundant manipulators without using joint torque sensors or wrist-mounted force/torque sensors. By using motor current measurements an estimation of the external forces acting on the manipulator can be obtained and allows for a compliant behavior. Joint friction effects are overcome by superposing an additional movement in the null-space of the end-effector task. This control scheme is applied to an industrial manipulator, namely a Stäubli TX90L mounted on a linear axis (constituting a redundant 7-DOF manipulator) and experimental results are provided.

Minimum-time trajectories for applications where a geometric path is followed by a kinematically redundant robot's end-effector may yield economical improvements in many cases compared to conventional manipulators. While for non-redundant robots the problem of finding such trajectories has been solved, the redundant case has not been treated exhaustively. In this contribution, the problem is treated as two interdependent subproblems: inverse kinematics and trajectory optimization. Therein, a differential inverse kinematics resolution scheme is augmented by adding an optimal linear combination of nullspace basis vectors of the corresponding velocity Jacobian. Using the practical example of an industrial robot with 7 degrees of freedom performing a 5 degrees of freedom task, the effectiveness of the presented method is shown. Comparisons are made with a joint space decomposition inverse kinematics resolution approach.

The use of more than one steerable (standard) driving wheel allows a robot to perform omnidirectional motions. However, the modeling and control of such robots is challenging since the system is non-holonomic, nonlinear and typically over actuated. Moreover, such platforms exhibit kinematic singularities. A well known singular configuration is the configuration where two steerable driving wheels are coaxial aligned. This is highly problematic since this configuration corresponds to pure rotations, which is crucial for narrow space navigation. In this paper a control scheme with improved robustness w.r.t. these singularities is derived. It is based on the second order (accelerations) non-holonomic constraints. The remaining singularity is tackled by a regular parametrization of the robot's motion. Thereupon a novel control concept is presented which is based on an input-output linearization in terms of a path parameter. The choice of this parametrization provides an additional parameter in the controller design. The approach is demonstrated for a prototype implementation.

For stable walking of bipedal robots it is necessary to stabilize the unactuated degrees of freedom of the robot. Typically this is done by reducing the non-linear multi-body dynamics to a simple approximation and then controlling the linear momentum of the system. In this paper a feedback controller is proposed that also controls the angular momentum in a feedback loop while considering the full multi-body dynamics to extend the set of balanced states.