Abstract Tensors are used to describe complex physical processes in many applications. Examples include the distribution of stresses in technical materials, acting forces during seismic events, or remodeling of biological tissues. While tensors encode such complex information mathematically precisely, the semantic interpretation of a tensor is challenging. Visualization can be beneficial here and is frequently used by domain experts. Typical strategies include the use of glyphs, color plots, lines, and isosurfaces. However, data complexity is nowadays accompanied by the sheer amount of data produced by large‐scale simulations and adds another level of obstruction between user and data. Given the limitations of traditional methods, and the extra cognitive effort of simple methods, more advanced tensor field visualization approaches have been the focus of this work. This survey aims to provide an overview of recent research results with a strong application‐oriented focus, targeting applications based on continuum mechanics, namely the fields of structural, bio‐, and geomechanics. As such, the survey is complementing and extending previously published surveys. Its utility is twofold: (i) It serves as basis for the visualization community to get an overview of recent visualization techniques. (ii) It emphasizes and explains the necessity for further research for visualizations in this context.

Modern engineering uses optimization to design long-living and robust components. One part of this process is to find the optimal stress-aware design under given geometric constraints and loading conditions. Tensor visualization provides techniques to show and evaluate the stress distribution based on finite element method simulations. One such technique are hyperstreamlines. They allow us to explore the stress along a line following one principal stress direction while showing the other principal stress directions and their values. In this paper, we show shortcomings of this approach from an engineer’s point of view and propose a variant called tensor spines. It provides an improved perception of the relation between the principal stresses helping engineers to optimize their designs further.

Scientific visualization developed successful methods for scalar and vector fields. For tensor fields, however, effective, interactive visualizations are still missing despite progress over the last decades. We present a general approach for the generation of separating surfaces in symmetric, second-order, three-dimensional tensor fields. These surfaces are defined as fiber surfaces of the invariant space, i.e. as pre-images of surfaces in the range of a complete set of invariants. This approach leads to a generalization of the fiber surface algorithm by Klacansky et al. [16] to three dimensions in the range. This is due to the fact that the invariant space is three-dimensional for symmetric second-order tensors over a spatial domain. We present an algorithm for surface construction for simplicial grids in the domain and simplicial surfaces in the invariant space. We demonstrate our approach by applying it to stress fields from component design in mechanical engineering.

Conventional skid or wheel based helicopter landing gears severely limit off-field landing possibilities, which are crucial when operating in scenarios such as mountain rescue. In this context, slopes beyond 8° and small obstacles can already pose a substantial hazard. An adaptive landing gear is proposed to overcome these limitations. It consists of four legs with one degree of freedom each. The total weight was minimized to demonstrate economic practicability. This was achieved by an innovative actuation, composed of a parallel arrangement of motor and brake, which relieves the motor from large impact loads during hard landings. The loads are alleviated by a spring-damper system acting in series to the actuation. Each leg is individually force controlled for optimal load distribution on compliant ground and to avoid tipping. The operation of the legs is fully autonomous during the landing phase. A prototype was designed and successfully tested on an unmanned helicopter with a maximum take-off weight of 78 kg. Finally, the implementation of the landing gear concept on aircraft of various scales was discussed.

Despite intensive investigations in the past, energetic efficiency is still one of the most important unsolved challenges in legged robot locomotion. This paper presents an unconventional approach to the problem of energetically efficient legged locomotion by applying actuation for spring mass running. This approach makes use of mechanical springs incorporated in parallel with relatively low-torque actuation, which is capable of both accommodating large payload and locomotion with low power input by exploiting self-excited vibration. For a systematic analysis, this paper employs both simulation models and physical platforms. The experiments show that the proposed approach is scalable across different payload between 0 and 150 kg, and is able to achieve a total cost of transport of 0.10, which is significantly lower than the previous locomotion robots and most of the biological systems in the similar scale, when actuated with the near-to natural frequency with the maximum payload.

For legged devices, their ability of carrying payload is a necessity for a wide range of tasks. In this paper, we present a new approach of carrying payload by using a parallel elastic mechanism, which is able to carry payloads of at least 3 times of its bodyweight. Although the robot has no sensory feedback and consists of only two rigid bodies and one spring loaded joint, it is able to achieve efficient and stable forward hopping for a wide range of attached payload. The presented payload carrier ETH Cargo is based on the further development of our platform CHIARO for the payload range between 0 and 100kg. After parameter optimization using simulations, a series of real world experiments prove stable and high efficiency hopping of the prototype over a wide range of payloads.

Reduction of the system complexity is currently one of the main challenges for efficient and versatile legged robot locomotion. In this paper, we present a new one legged hopping robot called CHIARO, which is equipped with a curved foot. Even though the robot has no sensory feedback and consists of only two rigid bodies and one spring loaded joint with parallel actuation, it is able to achieve stable forward-hopping over a wide range of parameters and forward-speeds. Operating at natural hopping frequency, the parallel actuation shows good efficiency. This paper presents an approach to determine stability and efficiency of a highly non-linear mechanical system. By implementing a two dimensional numerical model, taking into account ground contact forces by a Newtonian kinematic impact- and coulomb friction law, we conducted a thorough parameter analysis based on a series of simulations. The comparison of the simulation and real world experiments shows good accordance, which qualifies the simulation for parameter optimization including prediction of robot stability and efficiency.

For more dexterous and agile legged robot locomotion, alternative actuation has been one of the most long-awaited technologies. The goal of this paper is to investigate the use of newly developed actuator, the so-called Linear Multi-Modal Actuator (LMMA), in the context of legged robot locomotion, and analyze the behavioral performance of it. The LMMA consists of three discrete couplings which enable the system to switch between different mechanical dynamics such as instantaneous switches between series elastic and fully actuated dynamics. To test this actuator for legged locomotion, this paper introduces a one-legged robot platform we developed to implement the actuator, and explains a novel control strategy for hopping, i.e. “preloaded hopping control”. This control strategy takes advantage of the coupling mechanism of the LMMA to preload the series elasticity during the flight phase to improve the energy efficiency of hopping locomotion. This paper shows a series of experimental results that compare the control strategy with a simple sinusoidal actuation strategy to discuss the benefits and challenges of the proposed approach.

This paper presents a novel underwater robot based on biological locomotion principle. A robotic platform imitating sea-turtle fin propulsion is described and tested. As fin locomotion is a novel and complex research area, basic control concepts are analyzed and implemented. Based on a simulation, a fin-trajectory morphing control strategy is developed in order to control the robots roll, pitch and yaw rates, thus allowing the robot to follow a given vector. Absolute position control or depth control, however, is not yet implemented. The paper concludes with the presentation of a working system that demonstrated motion capabilities in air as well as the first dive test in a swimming pool.

Due to technological limitations robot actuators are often designed for specific tasks with narrow performance goals, whereas a wide range of output and behaviours is necessary for robots to operate autonomously in uncertain complex environments. We present a design framework that employs dynamic couplings in the form of brakes and clutches to increase the performance and diversity of linear actuators. The couplings are used to switch between a diverse range of discrete modes of operation within a single actuator. We also provide a design solution for miniaturized couplings that use dry friction to produce rapid switching and high braking forces. The couplings are designed so that once engaged or disengaged no extra energy is consumed. We apply the design framework and coupling design to a linear series elastic actuator (SEA) and show that this relatively simple implementation increases the performance and adds new behaviours to the standard design. Through a number of performance tests we are able to show rapid switching between a high and a low impedance output mode; that the actuator's spring can be charged to produce short bursts of high output power; and that the actuator has additional passive and rigid modes that consume no power once activated. Robots using actuators from this design framework would see a vast increase in their behavioural diversity and improvements in their performance not yet possible with conventional actuator design.