 ability to generalize and adapt learned motor behaviors. \fvc{For example, the concepts of `internal models' and `optimal control' can capture significant features of motor behavior, but it has been challenging to associate these theoretical frameworks with specific anatomical structures or physiological mechanisms. } It is only natural that some of these models have been inspired by the formalism and successes of robotics and control theory, which in turn have been influential in driving experimental approaches and theoretical frameworks (for review, see \cite{Wolpert2011}). 

However, even a cursory comparison between how robotic and human hands reach, grasp and manipulate objects reveals major differences between them. Some differences stem from ability of the neuromuscular system to implement versatile transitions, adjustments and adaptations of control strategies. One example is the ability of the hand to swiftly change control strategies when transitioning from finger motion to force application \cite{Venkadesan2008Neural}. Another example is humans' ability to modulate finger force distribution shortly after contact and prior to onset of manipulation to account for trial-to-trial variability in finger placement \cite{Fu2010,Fu2011,Fu2014a,Fu2014,Marneweck2016}. Such problems are extremely challenging to replicate in a robotic system. Other differences emerge from the hand's unique anatomical structure, which allows it to adapt to task demands, including passively shaping itself to object geometry. These are differences that robotic designs can partially address (see section `Under- vs. Over-actuated control'), but cannot fully match given the limitations of robotic systems in actively integrating sensory feedback with motor commands, or passively adapting to objects and the environment.

\subsection*{\fvc{Advantages and limitations of control theoretic approaches to biological sensorimotor control}}

These fundamental differences motivate and justify a candid evaluation of the extent to which our conceptual approaches to robotics are appropriate for the study of sensorimotor \fvc{control} in biological systems.  As mentioned above, the approach to biological sensorimotor \fvc{control}  has, for historical and practical reasons, leveraged the formalism of robotics and control theory (e.g., \cite{murray1994mathematical,valero2015fundamentals,Yamaguchi1990,shadmehr2012biological}). At the risk of oversimplifying a large field for the sake of succinctness, we can describe real-time feedback control as follows: sensors transduce physical signals to estimate the performance of the system, which the controller considers as it applies control laws to take the next actions to correct mistakes, reject perturbations, and meet the constraints of the task to achieve a goal. It stands to reason that the neuromuscular control of biological systems can perform all of these functions.  Therefore, \fvc{control-theoretic} constructs likely apply (e.g., \cite{todorov2002optimal,scott2004optimal,loeb1999Hierarchical,loeb1990understanding,peterka2002sensorimotor}). Such an approach is justified by the successes in identifying neural circuits that perform closed-loop feedback control such as homeostasis in physiological control systems \cite{khoo2000physiological}, muscle stretch reflexes \cite{mcintyre1993servo}, and vestibulo–ocular reflexes for eye tracking in the presence of head rotation \cite{angelaki2008vestibular,ranjbaran2015hybrid}.

Why is it that such a well-founded approach has failed to produce conclusive theories for sensorimotor control in humans for grasp and manipulation?\footnote{One can argue that work in invertebrates or locomotor patterns in vertebrates has been more successful, e.g., \cite{suver2016sensory,harris2010general,grillner2006biological}.}  One possibility is that sensorimotor control for grasp and manipulation is unlike other forms of motor control because its motor actions involve perception, as well as more complex sensorimotor transformation processes than, say, cyclical movements for  locomotion. The importance of the interaction between perception and action has been convincingly argued by, for example, Prinz, Iberall and Arbib \cite{iberall1990schemes,mackenzie1994grasping,mechsner2001perceptual,charpentier1891analyse}. This is further exemplified by other work bridging this perception-action gap \cite{yue1992strength,gordon1993memory,murray1999charpentier,flanagan2000independence,warren2011effects,craje2013effects}.

This conceptual divergence across biological and robotics problems can perhaps be explained by assessing some fundamental features of the robotics perspective, and their appropriateness for the study of sensorimotor \fvc{control}  in biological systems. Earlier, we spoke of the \fvc{control-theoretic} framework that defines interactions among sensors, control laws and the goal of the task.  A more formal presentation is that the control laws operate to change the `state' of the system. The formal definition of the state of a system is the minimal set of variables to characterize its governing equations, or that can be used to describe its dynamical evolution \cite{ogata1997,bryson1975applied,murray1994mathematical}. Thus, control theory is based on actions that will effectively and appropriately change the state to reach a goal, track an external process or reject a perturbation on the basis of a user-defined optimization criterion (often called objective or cost function). In fact, the definition of `controllability' is to be able to arbitrarily move a system from any state to any other state in finite time. Its counterpart is  `observability,' which is the formal quantification of the ability to arbitrarily extract the state of the system from measurements obtained by sensors \cite{kalman1959general,kalman1963mathematical}. When designing a robotic system, its state variables are explicitly chosen by the user from the many potential options, such as joint angles, angular velocities, endpoint locations, velocities, etc. Implementing observability via methods of state estimation is a form of system identification that spans a wide set of techniques, and which is central to any \fvc{control-theoretic} approach applied to robotics and models of biological function \cite{simon2006optimal,bryson1975applied,valero-cuevas2009computational}.

The field of neuromuscular control has come to the realization that it is still an open question whether and how the nervous system adopts the concept of state, and even whether it optimizes an explicit or implicit cost function \cite{deRugy2012muscle,loeb2012optimal,valero2015fundamentals}. This realization has been slow and reluctant because abandoning the sound engineering formalism is both unappealing and unnecessarily extreme. Thankfully, the past several decades have seen, as described below, the development of  equally well-founded alternatives or complements to the classical control theoretic perspective that mitigate the drawbacks of  state estimation, cost functions and even control laws. Furthermore, there are many other techniques and approaches that have yet to be applied to biological problems \cite{valero-cuevas2009computational}.

\subsection*{Feasible rather than optimal function}				
Optimization is a computationally efficient means to use convex, preferably quadratic, cost functions to select a specific control action from among all feasible actions within a high-dimensional solution space. For example, if you have N muscles crossing a joint, optimization can be used to search an N-dimensional space to find a point in it (i.e., a combination of muscle activations) to produce a given net joint torque while minimizing, say, the sum of squares of activations.

\fvc{Roboticists have always used optimization to control robots. Be it to tune gains in the P, PD or PID controllers  to implement force, impedance and position control \cite{ogata1997}, plan paths (e.g., \cite{shiller1989robot}), etc. In fact, the ubiquitous use of state estimators (such as Kalman Filters) are, in fact, optimal solutions in the least-square sense \cite{strang2003introduction}. In addition, this emphasis on optimality is central to \emph{Optimal Control} \cite{bryson1975applied} in its various modern forms as LQR, LQG, iLQR, iLQG (e.g., \cite{aschepkov2016optimal}.). From its inception, however, the emphasis on optimality has proven problematic to stability margins, which has led to other forms of control such as robust control, path integral control, model predictive control, etc. \cite{doyle1978,safonov2012origins,morari1993model, TheodorouJMLR}.}

Biomechanists and neuroscientists have, \fvc{ nevertheless, adopted the well-founded mathematical concept of optima} to cast the problem of neuromuscular  control as one of numerical optimization \cite{todorov2002optimal,Chao1978Graphical,crowninshield1981physiologically}. However, it is unlikely  that  the nervous system acts strictly like a computer running optimal control, gradient descent or policy gradient algorithms. Rather, optimization has and should be used as a metaphor, but one that should not be taken too literally when working with biological systems \cite{deRugy2012muscle,loeb2012optimal}.

We must recognize that, as with any metaphor, there are limits to its validity. It is important to explicitly acknowledge a bifurcation in the approaches we use to build robots vs. understand biological systems. For example, recent advances in control have begun to yield very impressive real-time performance in physical robots  \cite