A Human Augmentation Approach to Gait Restoration

Fig. 13.1

Emerging behaviors, arising from the coupled dynamics of human body and robotic structure interacting with the environment, help the execution of a complex task with low computational efforts. Low-level adaptations to the environment are managed by the intrinsic properties of the mechanical structure of the robot (preflexes)

Specifically, design for symbiosis is intended as a kind of design for emergence aiming at producing dynamic behaviors, by augmenting wearer’s residual motor capabilities, as useful to a given purpose (e.g. restoring proper motor abilities in chronic subjects, of whom elderly people are the most socially relevant example).

It is also desirable that the mechanical structure of the WR is capable of managing the low-level issues related to the interaction with the environment by exhibiting proper zero-delay, intrinsic responses (i.e. preflexes) to a perturbation [4]. The ability of a mechanical structure of producing useful emergent behaviors and of adapting itself to external perturbations through preflexes can be seen as whole as a form of structural intelligence, as an instantiation of embodied intelligence.

The concept of embodied intelligence highlights how intelligence benefits also from the physicality of an agent, where the term physicality is meant to catch as a whole the dynamic, kinematic and somesthetic properties of an organism and the typology of its possible interactions with the environment. Indeed, it is recognized [5] that the embodiment of an agent has implications on the information theoretic processes (e.g. by effectively structuring the sensory inflow from the environment) and that morphology itself can perform computation through physical interactions (i.e. morphological computation). Robots designed to exploit embodied intelligence are frequently simpler, more robust and adaptive than those based on the classical interaction control paradigm.

These concepts formulated in artificial intelligence and computer science are often strictly related with biological observations of animal behavior, especially in locomotion, that focus on the intimate connections among intelligence, morphology and performance. As shown in Kubow and Full [4], the lowest level of intelligence is completely physical, as it consists in the ability of neuro-musculoskeletal systems to present zero-delay, intrinsic responses to a perturbation [6]. Preflexes are useful for performing low-level tasks, such as stabilization and feedforward locomotion control. As an example, the cockroach Blaberus discoidalis is able to scramble over randomically distributed obstacles up to three times its body height without significantly slowing down [7]. Such striking performance cannot be achieved by a feedback-based, centralized sensory-motor control, because the required adaptation to the environment is too quick. On the contrary, robust locomotion is achieved mainly through a basically feedforward pattern applied to a properly tuned mechanical system. Such principles have been implemented in the development of a highly efficient hexapedal robot capable of sensorless robust locomotion at speeds up to 2.5 body lengths/s [8].

On a higher level, recent studies on biped robots have shown that even complex tasks, such as walking, may arise from the intrinsic dynamics of a machine during its interaction with the environment. Studies on passive walking show that bipedal walking, normally obtained through computationally demanding feedback control algorithms, can emerge from an accurate tuning of the dynamical properties of a purely mechanical system, without any feedback control [9, 10]. The performance obtained through this methodology produces a gait that appears to be more biomimetic under both the energetic and kinematic standpoints. In particular, it has been demonstrated that the energetic efficiency of such mechanisms is closer to that of the human body, while existing bipedal walking robots are about 30 times more energy demanding [11]. Moreover, experiments performed on physical simulation environments have shown that it is possible to optimize, via a coupled evolutionary process, both the morphological properties of a robot and its controller, with mutual benefits for both, in terms of reduced complexity and enhanced efficiency [12].

The two examples mentioned above demonstrate that better performance, with lower computation cost and with simpler and lighter structures, can be achieved if the potentialities of structural intelligence are properly harvested and exploited. Till now, such concepts have been explored and applied to the development of robots inspired by a large variety of biological systems, such as mammalians, fishes and insects. On the contrary, the human body has been poorly investigated from the structural intelligence standpoint, while this is a promising new route toward the development of useful machines intended for the strict interaction with humans, such as robots for rehabilitation, assistance and functional restoring for elderly and disabled people.

In the scenarios where the robot and the human body are strictly interacting, the design of the artificial system must take into account the dynamics of the biological counterpart, which is highly variable and actively tuned by the human sensory-motor system. When strict physical interaction occurs, the dynamics of the human body and that of the robotic artifact are strongly coupled. If the robot is meant to compensate for lost body functionalities, such as proper gait generation, the proposed approach consists in finding how the robotic system must be designed to take advantage of the variable biomechanical properties of the human body.

The objective is to design the robotic system in such a way that the dynamics of the human body, especially in the case of impaired or elderly subjects, and that of the robot during interaction, symbiotically benefit from each other, eliciting emergent dynamic behaviors, which favor the execution of the desired task.

The nature and the level of symbiosis, that can be effectively attained, depend on the specific employed design methods and tools and on their capability to accurately predict the kind of interaction that the user and the robot would establish, depending from the morphological and control properties of the latter.

The engineering of a specific dynamical interaction is still an open research objective. Indeed, it requires simulation tools not yet available, which should be capable to accurately model personal motor styles, human motor control strategies and time-dependent, subject-specific self-adaptations to the robot. Nonetheless, as presented in the following sections, the concept of structural intelligence can be effectively exploited to design a WR with a diverse structure, better ergonomics (i.e. intrinsically capable of solving micro- and macro- misalignments issues), better dynamical properties (e.g. limited inertial effects associated to the swinging of actuators), and good backdrivability.

The approach, in which embodied intelligence is taken a step further to embrace also the potentialities of structural intelligence, is radically new, as better highlighted by the analysis of the state of the art in the field of WRs, as summarized in the following section.

13.2 Wearable Robots for Gait Restoration

A substantial push in the advancements of the field of wearable robots for human performance augmentation has been provided by the program promoted by the US Defense Advanced Research Projects Agency (DARPA), called Exoskeletons for Human Performance Augmentation (EHPA), started in 2001, which encouraged the development of exoskeletons helping soldiers to carry backpacks during operative missions. The Berkeley Lower Extremity Exoskeleton (BLEEX) has been developed by prof. Kazerooni and his group at the University of California [13]. BLEEX features three Degrees Of Freedom (DOFs) at the hip, one at the knee, and three at the ankle. Of these, four are actuated: hip flexion/extension, hip abduction/adduction, knee flexion/extension, and ankle flexion/extension. Of the non-actuated joints, the ankle inversion/eversion and hip rotation joints are spring-loaded, and the ankle rotation joint is completely free [14].

After the first prototypal version of the system, the Berkeley Robotics & Human Engineering Laboratory worked on new versions of the device for military applications developing the ExoHiker and the ExoClimber systems, tailored for load carrying during overground walking or during slopes ascent. The third generation of their exoskeletal system, the Human Universal Load Carrier (HULC) has reduced bulkiness and weight, since structural parts are titanium made. Interestingly, the HULC is claimed to be the first system able to provide a reduction in the order of 5–15 % of the metabolic cost associated to overground walking.

Sarcos (recently purchased by Raytheon) has developed an exoskeleton also based on hydraulic actuation. The exoskeleton (Sarcos XOS) has been designed to encompass the entire body. The XOS robot includes 30 actuated DOFs and is controlled using a number of multi-axis force-moment transducers that are located between the feet, the hands and the torso of the operator and the machine [15]. However, the largest drawback of this device is the lack of a mobile power source. A quasi-passive exoskeleton, the MIT exoskeleton, has been designed in the Biomechatronics Group at the Massachusetts Institute of Technology Media Laboratory by the group of prof. Hugh Herr. This concept seeks to exploit the passive dynamics of human walking in order to create a lighter exoskeletal device [11], which demonstrated an increased energetic efficiency when compared to conventional walking machine designed through a kinematically anthropomorphic design and controlled via Zero Moment Point (ZMP) technique [16, 17]. The group of prof. Yoshiyuki Sankai at the University of Tsukuba (Japan) developed an exoskeleton targeted for both performance-augmenting and rehabilitative purposes [18, 19]. The leg structure of the full-body HAL-5 exoskeleton powers the flexion/extension of hip and knee joints via a DC motor with harmonic drive placed directly on the joints. The ankle dorsi/plantar flexion DOF is passive. The HAL-5 system utilizes a number of sensing modalities: skin-surface EMG electrodes, placed below the hip and above the knee on both the anterior (front) and posterior (back) sides of the wearer’s body; potentiometers for joints angles measurement, ground reaction force sensors, a gyroscope and accelerometer mounted on the backpack for torso posture estimation. HAL-5 is currently commercialized by the spinoff company Cyberdine (Tsukuba, Japan).

Compared to human augmentation devices, mobile medical exoskeletons are intended for assistive and/or rehabilitative purposes. Improving the quality of life of wheelchair users is the aim of the Ekso, designed and commercialized by the Ekso Bionics (Berkeley, CA, US), intended for people with lower extremity weakness or paralysis due to neurological disease or injury (spinal cord injuries, multiple sclerosis, Guillain Barré syndrome).

Founded in 2001 and originally operating under the auspices of the Technion Seed (Technion, Institute of Technology, Israel), Argo Medical Technologies has developed a robotic ambulation system for wheelchair users named ReWalk, assisting only the movements in the sagittal plane. The ankle joint is not actuated.

Different from Ekso and ReWalk, REX, produced by REX Bionics (Auckland, New Zealand), is an anthropomorphic lower body orthosis designed for sit-to-stand, stair ascend and overground walking, without the use of crutches. The system does not use sensors to sense the intention of the user but uses a joystick for the user to control the exoskeleton. The system has been validated with healthy subjects, and for sit-to-stand of wheelchair users.

The Vanderbilt powered orthosis [20] is a powered lower-limb orthosis intended for Spinal Cord Injured (SCI) individuals. Differently from the previous mentioned devices, it neither includes a portion worn over the shoulders, nor a portion under the shoes. The orthosis is intended to be used in conjunction with a standard ankle foot orthosis, which provides support at the ankle and prevents foot drop during swing.

Treadmill-based WRs are mainly used as rehabilitation platforms capable of (partially) supporting patient weight and of providing assistance in performing therapeutic exercises, usually according to the Assist-As-Needed (AAN) paradigm.

Lokomat, developed by Hocoma (Volketswil, Switzerland), assists hip and knee movements in the sagittal plane while the ankle joint is not supported. Similarly, the LOPES (LOwer-extremity Powered ExoSkeleton) is a treadmill-based wearable robotic device for gait training and assessment of motor function in stroke patients [21] developed at University of Twente by the group led by prof. Herman van der Kooij. It is comprised of two parts: the adjustable lightweight frame for pelvic control actuating the two horizontal pelvis translations and the exoskeleton leg with four actuated DOFs per each leg which assist hip flexion/extension, adduction/abduction, knee flexion/extension and ankle dorsi/plantar flexion. All the actuated DOFs are based on series elastic actuation, consisting of a servomotor, a flexible Bowden cable transmission and a force feedback controller. This solution implies that the actuators are used as force (and torque) sources and allow impedance control of the robot. Impedance control with this kind of setup can be used in both high impedance control (resembling position control) and zero impedance control.

The AutoAmbulator [22] by Healtsouth Corp. (AL, USA) essentially consists of an electrically actuated anthropomorphic device supporting hip and knee movements in the sagittal plane.

The Pelvic Assist Manipulator (PAM) and Pneumatically Operated Gait Orthosis (POGO) are pneumatic robots that compliantly assist in gait training. PAM can assist in five DOFs of pelvic motion, while POGO can assist the hip/knee flexion/extension [23]. The devices can be used in a back-drivable mode to record a desired stepping pattern that is manually specified by human trainers, then replay the pattern with compliant assistance. During compliant replay, the devices automatically synchronize the timing of the replayed motions to the inherent variations in the patient’s step timing, thereby maintaining an appropriate phase relationship with the patient.

In some systems developed in the last years the principles of structural intelligence can be glimpsed. In Krut et al. [24], Mokhtarian et al. [25], Vallery et al. [26] passive spring-based balancers dynamically sustain the body weight during walking. In the MIT SkyWalker [27], passive walkers have provided inspiration to define gait rehabilitation strategies that promote natural legs dynamics during the swing phase. Another interesting example is the Elastic exoskeleton [28], developed at University of Michigan, where leaf springs provide intrinsic elasticity and allow an optimized human-robot energy exchange during running. In KNEXO [29] the principles of bioinspiration, as a form of embodied intelligence, has been exploited in the actuation system; the agonistic/antagonistic configuration of two pleated pneumatic artificial muscles has been adopted to actuate a knee orthosis for gait assistance.

The problem of assessing if, how and how much the findings achieved in the field of pseudo-passive bipedal walking can be transferred to the field of WRs for the lower limbs consists of a very tough challenge. Despite of that, the literature suggests that possible improvements of the performances of WRs can be provided by “opening” the design of the mechanical subcomponent, and not just focusing on novel control schemes or aspects related to actuators power efficiency or intrinsic safety.

These considerations suggest that WRs performances can benefit from a careful design of robot morphology, which is open in the case of non-anthropomorphic WRs, and can allow to achieve a better dynamical interaction with the human body and with the environment.

13.3 Non-anthropomorphic Design: From Topological Analysis to Morphological Optimization

The problem of optimal kinematic synthesis of non-anthropomorphic WRs may be very unpractical to be tackled by the conventional insight-driven engineering approach, due to the large number of open parameters involved in the design. This task can be simplified by automatic tools in support of the designer.

In the last decade, evolutionary programming has been applied to solve the problem of co-designing both the mechanics and the control of mobile artificial machines, by just defining the basic building blocks of the structure and the rules to connect them [30, 31]. This open-ended design methodology has the advantage that it can lead to unexpected design solutions. However, such kind of methods implies that the entire design process is completely demanded to the tool, which can autonomously decide to switch to a more complex structure during the optimization phase so to increase the fitness of the best individuals.

The authors are pursuing a systematic approach for the kinematic synthesis of WRs, based on a three-step process. The first step requires the exhaustive search of all independent generalized solutions for a WR design problem; the subsequent step consists of the selection among the pool of admissible solutions; finally, a candidate solution is optimized in terms of its morphological parameters, to satisfy a multi-objective fitness function.

This three-step strategy appears more reliable compared to open-ended kinematic optimization approaches, since optimization algorithms, acting on a fixed parameter space, are simpler and converge faster. Compared to the “brute-force” approach followed in [30], this strategy guarantees that only a reduced subset of solutions are evaluated, i.e. those kinematically compatible with the human body. Additionally, this strategy assures completeness: all relevant generalized solutions (i.e. topologies) are considered before producing the final design. The only drawback of the approach consists in the fact it requires the a-priori knowledge of the independent topologies having desired kinematic properties. No standard design tool was available for this specific problem of the design of a non-anthropomorphic WR for gait assistance, and then a major methodological step has been focused on development of ad-hoc computational tools, adapted from the general case of mechanism design.

13.3.1 Exhaustive Kinematic Synthesis of Non-anthropomorphic Wearable Robots

As a first step, it is important to define an efficient encoding, which allows the representation of the kinematic structure of a WR connected to a given human limb, which is modeled as a generalized serial chain. Since the aim is to evaluate also the mobility of the human limbs connected to the robot, the parallel kinematic chain, consisting of both robot links and human limbs, is considered. The most generalized level of abstraction at which such structure can be described is the topology level, which defines only the number of links and the connections among them.

13.3.1.1 Kinematic Structure Encoding and Topologies Enumeration

Under some reasonable hypotheses [32], many properties of mechanisms kinematics, such as the number of DOFs, are entirely determined only by the topology of the kinematic chain and unaltered by the geometry of its links. At this level of abstraction, the classical (graph)-(kinematic chain) analogy introduced in [33] can be employed, where graph vertexes correspond to the links of the chain and edges correspond to the joints. A graph can then be encoded through the Topology vertex-vertex Adjacency Matrix (TAM): a binary symmetric matrix of order n (where n corresponds to the number of links) where the element a _ijequals to 1 if link i and link j are connected through a joint, and to 0 otherwise.

As a first assumption, we decide to focus on planar kinematic chains composed of only revolute joints, for the assistance of the lower limb, modeled as a serial chain with three DOFs (hip, knee and ankle) moving in the sagittal plane. It is then unnecessary to discriminate on the type of joint connecting each link; hence the representation is complete in the description of kinematic chains topology, allowing the conversion of a problem of kinematic synthesis into a problem of graphs enumeration. The mentioned assumption limits the relevance of the methodology for the design of assistive WRs for the lower limbs, since the hip and the ankle joints have spatial movements. However, it can be noticed that, during ground walking, most of the power of the lower limbs is provided by actuation of movements in the sagittal plane, which is therefore the dominant plane during human locomotion [34].

The graph enumeration problem is graphically represented in Fig. 13.2, which depicts the structural representation, the graph representation and the corresponding TAM of the kinematic chain comprising both human segments and robot links. The process of enumerating kinematic chains consists of three successive steps: (i) enumeration of graphs with the desired mobility, (ii) pruning of isomorphic (i.e. non-independent) solutions and, (iii) pruning of non-kinematic compatible solutions. The mentioned steps will be described in more detail in the following.

Fig. 13.2

Structural representation (a), generalized TAM (b) and graph representation (c) of the problem of structural synthesis of robotic orthoses for a planar WR for the lower limbs. Human articulations and segments are in blue, while robot links and joints are in red. In the adjacency matrix, the blue color is used to represent entries which describe the connectivity of human limbs, while the red color represents fixed entries

Each kinematic solution can be represented by a graph with h + r edges, where h corresponds to the number of body segments (four in our case) and r corresponds to the number of robot links.

The complete list of independent kinematic solutions can be derived from the frame of the basic TAM shown in Fig. 13.2b. Any topology can be encoded by a binary string of length l, where:

$l= h\left( r- h\right)+\frac{r\left( r-1\right)}{2}$

(13.1)

However, not any combination of parameters is adequate, since we are interested only in kinematic chains with a given number of DOFs. For a given planar kinematic chain with n links and f joints with one DOF, the total number of degrees of freedom (DOFs) is obtained by using the Kutzbach criterion [35]:

$DOFs=3\left( n-1\right)-2 f$

(13.2)

From (13.2), given any number of links and a desired number of DOFs, the kinematic chain can contain only a fixed number of joints. Since each joint between links i and j corresponds to a 1 in the (i, j) position of the corresponding TAM, the problem of enumeration of all topologies with a desired mobility can be converted into the problem of exhaustively listing the binary strings of length l, with a fixed number of ones.

13.3.1.2 Degeneracy and HR-Degeneracy Testing

A further selection over the list of enumerated topologies is performed, in order to filter out the kinematic chains which:

contain rigid or over-constrained sub-chains;

correspond to disconnected graphs (i.e. not all graphs vertices are connected by a path);

impair the motion of human joints.

A standard degeneracy testing algorithm has been implemented to recognize and discard rigid sub-chains (such as three links-three joints and five links-six joints sub-chains). Kinematic chains containing at least one sub-chain with zero or negative DOFs according to Kutzbach formula (e.g. three links-three joints and five links-six joints sub-chains) are considered as degenerate solutions and are then eliminated. Additionally, disconnected mechanisms (i.e. such that there is not a path connecting each couple of vertices of the corresponding graph) are eliminated with a purposively developed algorithm, which verifies the existence of a path between each couple of vertices.

Furthermore, an additional test was introduced so to exclude those solutions where a subset of p human joints is part of a subchain with less than p DOFs. In this case the robot would impair human movements by imposing unnatural kinematic constraints. This test is called HR-degeneracy test (Human-Robot degeneracy test) since it applies to kinematic chains including both human and robot structures. The test is performed by recognizing the presence of sub-chains where two adjacent human joints are constrained in a one-DOF sub-chain, or where all three adjacent human joints are constrained in a two-DOFs sub-chain. The exhaustive list of such HR-degenerate primitives (reported in Fig. 13.2) could be obtained by adapting results coming from standard atlases of kinematic chains [36] and was re-obtained in a previous work concerning the enumeration of orthoses for a one-DOF human joint [37].

13.3.1.3 HR-Isomorphism Testing

Since the chosen method is based on the enumeration of suitable matrices of adjacencies, an explicit isomorphism test is required to guarantee mutual independence of set of enumerated solutions. Two kinematic chains K ₁ and K ₂ are said to be isomorphic if there exists a one-to-one correspondence between links of K ₁ and K ₂ such that any pair of links of K ₁ are jointed if and only if the corresponding pair of links of K ₂ are jointed. This means that from the graph corresponding to K ₁ one can obtain the graph corresponding to K ₂ by only relabeling link numbers.

A function defined on a kinematic chain is called an index of isomorphism if any given pair of kinematic chains is isomorphic if and only if the corresponding values of the function are identical. The index of isomorphism used in the present work is the characteristic polynomial of the Extended Adjacency Matrix (EAM) A ^(d)of order d, as also suggested in [38]. In [38] it is demonstrated that the simultaneous evaluation of the characteristic polynomial of both A ⁽⁰⁾, A ⁽¹⁾ and A ⁽²⁾ has a reliability of 100 % for kinematic chains consisting of up to 11 links. This technique for isomorphism detection shows to be a very good compromise between reliability and computational efficiency, since it requires a polynomial time for assessing isomorphism.

However, when applying the isomorphism test to kinematic chains including both human segments and robot links, any kind of isomorphism test produces false-positives, because robot and human links would be treated the same way. This happens because isomorphism tests are “blind” with respect to the special condition which involves considering both human segments and robot links as part of a unique kinematic chain. A false positive happens any time the permutation, which maps one graph into the other, affects any of the human joints. From the perspective of designing a WR aimed at a certain kind of interaction with each of the human joints, such solutions correspond to actual different WR topologies and must not be discarded. An example of two isomorphic but not HR-isomorphic solutions is shown in Fig. 13.3. To recognize such kind of solutions, a modified version of the isomorphism test has been introduced and named HR-isomorphism test (since it applies to kinematic chain including both human and robot structures). This test basically consists of assessing, after a classical characteristic polynomial-based isomorphism test, whether one of the permutations p _admcontained in a properly defined set P _admis responsible for mapping one kinematic chain into another. Every permutation vector contained in the P _admset is of the form p _adm(i) = [1 2 3 4 perms_i(5:n)], where the function perms _iprovides the i ^thelement of the set of permutations of the elements in the input array.

Fig. 13.3

Two isomorphic but not HR-isomorphic solutions. The permutation mapping K ₁into K ₂is given by the permutation vector [1 2 3 7 5 6 4 9 8]. This permutation maps link 4 (i.e. foot) into robot link 7. It can be noticed that local kinematic properties around each human joint (for example DOFs of the subchain including the hip, the knee and the ankle joints) are different in the two kinematic chains

13.3.2 Application to a Two-DOF Lower Limbs Wearable Robot for Hip and Knee Assistance

The developed method is applied to the design of the LENAR (Lower-Extremity Non-Anthropomorphic Robot) for hip and knee assistance in the sagittal plane. A design optimization is carried out to minimize static torques demanded to actuators to provide gait assistance. Due to the considerations reported above, the following hypotheses/constraints are imposed:

robot kinematic design is not fixed a-priori and can be possibly non-anthropomorphic;

only solutions involving revolute joints are considered;

the desired number of DOFs of the parallel structure, comprising both human segments and robot links, is two;

simultaneous and independent movements of the hip and the knee joints must not be constrained (i.e. the structure must not to impose unnatural kinematic constraints to the addressed human joints).

The method described in Sect. 13.3.1 allowed to exhaustively list all the independent kinematic structures of planar kinematically-compatible wearable hip-knee robotic orthoses, respecting the constraints reported above. Ten generalized solutions (topologies) are admissible in the considered design problem, as shown in Fig. 13.4. Such solutions represent the most synthetic form of describing the mechanical optimization problem described so far.

Fig. 13.4

(a) Arbitrary structural representation of the ten generalized solutions for the design problem addressed. Human segments are reported in blue, and human articulations are reported in black. Robot joints are reported in orange (on attachment sites) and in green (Adapted from [39]). (b) Kinematic scheme of the selected WR design (black), worn by a subject (gray). Actuated joints are joints A and joint D, that guarantee controllability of hip posture and knee posture with two DOFs

We applied a heuristic topology selection criterion based on a static ergonomics principle: correct force interaction in WRs is based on the transfer of forces to human segments only in the direction orthogonal to the bones. If the connection between a human segment and the robot is implemented through a binary passive link (i.e. with two passive revolute joints at its extremities), static forces applied on the human segments are necessarily directed along the connection link axis.

No forces along the orthogonal direction can be present, since no torque can be applied by passive joints. If said passive link is orthogonal to the human segment to which it is connected, the transfer of forces can be statically optimized based on simple geometric considerations (i.e. the attached link must be orthogonal to the addressed segment). Using this criterion, we investigated which of the ten topologies in Fig. 13.4 allowed links 5 and 6 (respectively connected to the thigh and shank) to be completely passive and orthogonal to human segments (labeled with 2 and 3). Three topologies (4, 6 and 10) guarantee in principle such condition, while still allowing independent control of hip and knee movements by actuating the two remaining joints. Topology 10 was finally selected, since it allows to reduce size and weight and to better distribute masses and inertias along the lower limb. A schematic of the resulting kinematic chain is shown in Fig. 13.4b.

13.3.2.1 Morphological Optimization of a Non-anthropomorphic Wearable Robot for Hip-Knee Assistance During Gait

A model of the chosen generalized solution was developed, as described in more detail in Sergi et al. [40], allowing to calculate the torques required to actuators to guarantee a physiological gait [34], for a generic set of parameters defining the structure shown in Fig. 13.4b. By using the mentioned model, morphological optimization was carried out, using a custom scalar fitness function, designed in order to take into account known limitations of actuators purposively developed for this wearable robot (Sect. 13.4), and in order to guarantee a high desired level of ergonomics of force interaction.

Using standard walking datasets reporting kinematic variables of level-ground walking (hip and knee angles θ _h(t) and θ _k(t)), as well as inverse-dynamics calculated equivalent torques exerted by subjects (hip and knee torques τ _h(t) and τ _k(t)), the corresponding actuator torques τ _m1(t) and τ _m2(t) and interaction forces at the points of contact A, B and C could be calculated. In particular, the components of interaction forces in contact points B (shank) and C (thigh) were decoupled into the component perpendicular to the connected body segment F _perpand the component parallel to it F _shear.

Workspace maximization was introduced as another optimization objective. In particular, increasing robustness of the design with respect to kinematic singularities was a highly sought design target, considered the specific application of the parallel WR. To this aim, passive angles values were individually checked for parallelism throughout the entire planar workspace of the robot. The occurrence condition of a singular configuration was that the angle between two passive links fell below a threshold, set to 30 ° in the optimization. Singularity is signaled by a binary variable sing(θ _h,θ _k). The posture at which a singular configuration occurred was taken into account, by specifying a singularity weighting function w _sing(θ _h,θ _k), designed to take into account the distance between the posture at which a singular configuration was detected and the nominal trajectory of the hip and knee joints during nominal gait, as shown in Fig. 13.5.