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Frontiers in Neurorobotics

We observe that human infants are born without the ability to reach, grasp, and manipulate nearby objects.

Their motions are seemingly aimless, but careful research has established that infants are biased toward moving objects and toward keeping the hands in view (von Hofsten, 1982, 1984;

After a few months of unguided experience, human infants can reach deliberately to contact nearby objects, and after a few more months, they can grasp nearby objects with a reasonable degree of reliability (Berthier, 2011).

During the early process of learning to reach, children's arm trajectories are quite jerky, suggesting the underdamped behavior of partially tuned control laws (Thelen et al., 1993).

However, an elegant experiment (Clifton et al., 1993) refutes this hypothesis by showing that young children's reaching behavior is unaffected when they can see the target object, but not their own hands.

During later reach learning, children and adults move the arm and hand more smoothly and directly to the target object, and they start depending on visual access to the moving hand (Berthier, 2011).

We abstract this developmental psychology problem to a problem in robot learning (Figure 1): How can a robot learn, from unguided exploratory experience, to reach and grasp nearby objects?

This paper focuses on learning from unguided exploration the functional relations linking proprioception and vision, two sensory modalities central to the representation of knowledge of peripersonal space.

Reaching and grasping are among the earliest actions learned by a human infant, and they help it achieve control over its immediate environment, by being able to grasp an object, take control of it, and move it from one position to another.

fundamental question about developmental learning is how an agent, without prior knowledge of its body, its sensors, its effectors, or its environment, can build a useful representation for the state of its world, and then can use this representation to learn reliable actions to change that state.

After creating the PPS graph, the process collects data about an initial action, learning its typical results, identifying unusual results, and then adding new preconditions or parameterizations to define a novel action that makes those unusual results reliable.

Given a block to reach, the learning process finds preconditions that identify a target PPS node corresponding to that block, so that moving to that target node reliably reaches the intended block.

Human infants, for several months after birth, exhibit the Palmar reflex, in which a touch on the palm causes the fingers to close tightly, automatically (and unintentionally) grasping an object (Futagi et al., 2012), the unusual event of an accidental grasp becomes frequent enough to provide sufficient data for a learning algorithm.

There is a rich literature in developmental psychology on how infants learn to reach and grasp, in which the overall chronology of learning to reach is reasonably clear (e.g., Berthier, 2011;

From about 15 weeks to about 8 months, reaching movements become increasingly successful, but they are jerky with successive submovements, some of which may represent corrective submovements (von Hofsten, 1991), and some of which reflect underdamped oscillations on the way to an equilibrium point (Thelen et al., 1993).

For decades, early reaching was generally believed to require visual perception of both the hand and the target object, with reaching taking place through a process of bringing the hand and object images together (“visual servoing”).

The smoothness of reaching continues to improve over early years, toward adult reaches which typically consist of “a single motor command with inflight corrective movements as needed”

Theorists grapple with the problem that reaching and grasping require learning useful mappings between visual space (two- or three-dimensional) and the configuration space of the arm (with dimensionality equal to the number degrees of freedom).

The second is capable of re-mapping spatial relations in light of changes in body posture and arm configuration, and thus effectively encodes object position in a world-centered frame of reference.

Their analysis supports two separately-developing neural pathways, one for Reach, which moves the hand to contact the target object, and a second for Grasp, which shapes the hand to gain successful control of the object.

We believe that a theory of a behavior of interest (in this case, learning from unguided experience to reach and grasp) can be subjected to an additional demanding evaluation by working to define and implement a computational model capable of exhibiting the desired behavior.

The early reaching trajectory will be quite jerky because of the granularity of the edges in the PPS Graph (von Hofsten, 1991), but another component of the jerkiness could well be due to underdamped dynamical control of the hand as it moves along each edge (Thelen et al., 1993), which is not yet incorporated into our model.

Sturm et al., 2008) focus on learning the kind of precise model of the robot that is used for traditional forward and inverse kinematics-based motion planning.

(2008) learn a body schema for a humanoid robot, modeled as a tree-structured hierarchy of frames of reference, assuming that the robot is given the topology of the network of joints and segments and that the robot can perceive and track the 3D position of each end-effector.

(2011) propose an architecture consisting of two radial basis function networks linking retinotopic information with eye movements and arm movements through a shared head/body-centered representation.

They demonstrate pre-reaching, gross-reaching, and fine-reaching phases of learning and behavior, qualitatively matching observations of children such as diminished use of vision in the first two phases, and proximal-then-distal use of the arm's degrees of freedom.

The transitions from one phase to the next are represented by manually adding certain links and changing certain parameters in the network, begging the question about how and why those changes take place during development.

(2014) present a computational model of reach learning based on reinforcement learning, equilibrium point control, and minimizing the speed of the hand at contact.

Model predictions are compared with longitudinal observations of infant reaching between ages of 100 and 600 days (Berthier and Keen, 2006), demonstrating qualitative similarities between their predictions and the experimental data in the evolution of performance variables over developmental time.

Their focus is on the irregular, jerky trajectories of early reaching (Berthier, 2011), and they attribute this to sensor and process noise, corrective motions, and underdamped dynamics (Thelen et al., 1993).

By contrast, we attribute part of the irregular motion to the irregularity of motion along paths in the PPS graph (rather than to real-time detection and correction of errors in the trajectory, which would be inconsistent with Clifton et al., 1993).

We accept that other parts of this irregularity is likely due to process noise and underdamped dynamics during motion along individual edges in the PPS graph, but that aspect of our model is not yet implemented.

At the same time, the graph representation we use to represent early knowledge of peripersonal space can handle a realistic number of degrees of freedom in a humanoid robot manipulator (Figure 1).

Several recent research results are closer to our approach, in the sense of focusing on sensorimotor learning without explicit skill programming, exploration guidance, or labeled training examples.

Within our framework, the Reachable Space Map would be a valuable addition (in future work), but the PPS Graph (Juett and Kuipers, 2016) is learned at a developmentally earlier stage of knowledge, before goal-directed reaching has a meaningful chance of success.

The PPS Graph is learned during non-goal-directed motor babbling, as a sampled exploration of configuration space, accumulating associations between the joint angles determining the arm configuration and the visual image of the arm.

Composing these defines a (partial) function g that the robot can learn about, by simultaneously using proprioception to sense the configuration q, and visual perception to sense the image Ip.

From an initial pose q0 in an empty environment, the robot samples a sequence of perturbations Δq from a distribution D to generate a sequence of poses: While the motor babbling of human infants may appear random, it does exhibit biases toward moving objects and toward keeping the hand visible (von Hofsten, 1982, 1984;

After each new pose has been safely reached by physical motion of the arm, a corresponding perceptual image Ip,i+1 is collected, and the node ni+1 = (qi+1, Ip,i+1) and the undirected edge ei,i+1 = (ni, ni+1) are added to P.

By searching the information in the PPS graph P, we can define a function h that provides a discrete approximation to g−1 from Equation (3): Given a current visual image Ib of an object (e.g., a block) in the environment, we can identify nodes (q, Ip) = n ∈

The generic operator selectq defines the role for a criterion for selecting among matching nodes, for example by maximizing the overlap between binary images Ib and Ip, or by minimizing the distance between their centers.

For our experiment, we apply the methods described above (section 3.1) to learn to control the left arm of our Baxter Research Robot (Figure 1), providing specific instantiations for the generic aspects of the method.

We impose a bias using a form of rejection sampling, requiring that the resulting end-effector pose must fall within the field of view, and must not collide either with the table or with the robot's own body.

To prevent damage to our Baxter Research Robot, we implement these checks using a manufacturer-provided forward kinematics model that is below the level of detail of our model, and is used nowhere else in its implementation.

To move along an edge eij from ni to nj, in the current implementation, the agent uses linear interpolation of each joint angle qk from its value in qi to its value in qj.

It is evident that random sampling through unguided exploration has distributed N = 3, 000 nodes reasonably well throughout the workspace, with some localized sparse patches and a region in the far right corner that is generally out of reach of the robot's left hand.

First, the agent must learn to detect the unusual event of bumping a block, causing a quasi-static change in the environment, against the background of typical arm motions that leave the environment unchanged.

The blocks are placed upright at randomly generated coordinates on the table in front of the robot, with the requirement that each placement leaves all blocks unoccluded and fully within the field of vision.

The palm mask pi is defined to be the region between the gripper fingers, which will be most relevant for grasping.2 The hand mask hi includes this region as well as the gripper fingers and the wrist near the base of the hand.

Edges can also be associated with a binary mask for the area swept through during motion along it, si,i′, approximated by a convex hull of the hand masks of the endpoint nodes, hi and hi′.

However, in a rare event the hand bumps the object, knocking it over, or sliding it along the table and sometimes off the table (the resulting absence of a final mask leads to an IOU of 0, so no special case is necessary).

While we human observers can describe the smaller cluster as a bump event, the robot learning agent knows only that the smaller cluster represents an unusual but recognizable event, worth further exploration.

For a node ni, the center of the palm cip is composed of the center of mass of pi and the average depth, mean(PD(ni)[pi]), and the center of the hand cih is derived from hi and PD(ni)[pi] in the same manner.

By further analysis of the data reported in section 4.1.3 from 102 reaching trajectories, the agent can determine which binary image mask, and which intersection property, best predict whether a trajectory will produce a bump event.

The set of PPS graph nodes that satisfy the selected mask intersection property, with the best choice of mask, will define the set of candidate final nodes for a reach trajectory.

An improved reach action policy can be created by selecting the target node nf as a random member of the candidate final node set, rather than a random node from the entire PPS graph.

This policy is evaluated using the same method as Experiment 2 in section 4.1.2: reaching for 40 blocks, presented individually at randomly assigned locations on the table.

To address this issue, we identify a distance measure between hand and target object, and then select from the set of candidate nodes, the node that minimizes that distance measure.

Each array represents the four possible intersection conditions, and each entry holds the conditional probability of a bump event in a trajectory satisfying that intersection conditioned, explained as the ratio of bump events to trajectories.

bump is most likely (64%) to occur at a final node nf where the palm percept has a nonempty intersection in both mask and depth range with the target percept, that is, where The process of identifying a node as a candidate is demonstrated in Figure 4.

For the same 40 placements as the baseline (Experiment 2), 39 have at least one node with both mask and depth range intersections with the target (i.e., has a non-empty candidate final node set), and the policy of moving to one of these nodes bumps the target 21 times.

Attempting the 40 reaches again, the agent now considers the reach action to be 77.5% reliable, with 31 successes, 7 false negatives, and 2 actual failures to bump the object.

Tabulated results from experiments 3, 5, and 6: This method, for identifying candidate target nodes that increase the probability of bumping a specified block, can be extended to avoid bumping specified blocks.

Recall that the first improvement to the reach action was to identify a set of candidate final nodes, all nodes where the stored hand representation and the current percept of the target intersect in both the RGB and depth images.

The full Jacobian model J(q) relating joint angle changes Δq to changes in hand center coordinates Δc is a nonlinear mapping, dependent on the current state of the arm q, a seven-dimensional vector.

Conversely, given a desired change Δc in the appearance of the hand, the pseudo-inverse Ĵ+(ni) makes it easy to compute the change Δq in arm configuration that will produce that result.

3 matrix where the element at [row, col] gives the rate of change for ccol (either the u, v, or d coordinate of the palm's center of mass) for each unit change to qrow.

A possible adjustment Δq to qi may be evaluated by determining if the predicted new palm center ĉip≡cip+ΔqĴ(ni) and the palm mask pi translated by ΔqĴ(ni) have desirable features.

Where nf is the final node of the planned trajectory for a reach, the agent can use the local Jacobian Ĵ(nf) and its pseudo-inverse Ĵ+(nf) to improve the accuracy of its final motion, and the likelihood of causing a bump event.

While the ability to make a small move off of the graph to qf* increases the robustness of the reach, it does not eliminate the need for a set of candidate final nodes, or for the decision to use the nearest node to the target as nf.

In our model, after the intrinsic motivation pattern has resulted in a reliable reach action, the pattern may be applied a second time to learn a grasp action.

Driven by intrinsic motivation, the grasp action becomes more reliable, toward becoming sufficient to serve as part of a pick and place operation in high level planning.

Our agent then learned: how to most reliably set the gripper's aperture during the grasp approach, how to best align the hand, target, and final motion, and how to preshape the hand by orienting the wrist.

This gives a much greater level of control over the pose of the object, as it can be manipulated with the agent's learned scheme for moving the hand until the relationship ends with an ungrasp, opening the fingers to release the object.

The variety of outcomes possible with the level of control a grasp provides imply a high potential reward from learning to predict the outcomes and actions to cause them, but it is also the case that grasps occur too rarely to learn immediately after learning to reach.

When the hand's final approach to the target meets all necessary conditions of openness, alignment, and orientation, the target object passes between the grippers in a way that activates the simulated Palmar reflex, and the gripper fingers close.

A grasp is successful if and only if the stored masks and depth ranges for each node of the trajectory intersect with those of the target object in the visual percepts during the return to the home node.

By considering both situations to be failures, the successful grasps that emerge from this learning process are more likely to facilitate subsequent learning of higher order actions that require a grasp.

Each of the joint angles in q have an understood role in the placement of the hand, but a does not appear to significantly affect the location of the hand's center of mass and does not differentiate graph nodes.

We claim that this demonstrates the agent could have learned the reach action with the same process and ending reliability for any gripper setting, and at that point would learn to prefer 100% open.

To learn to use satisfactory relationships between these vectors, the agent constructs this set of vectors using information from its stored and current visual percepts: The agent learns cosine similarity criteria for the vectors of final motions that most reliably cause Palmar reflex activations in Experiment 10.

To discover the best relationship between these vectors for repeating the Palmar reflex activation event, the agent uses the data from repeating the final reach trajectories of Experiment 7 in Experiment 8 with the Palmar reflex enabled.

The three steps of choosing nf, adjusting to qf* to match centers with the target, and translating to create a well-aligned preshaping position with qp* are visualized in Figure 10.

The reliability of the grasp action using this method for planning trajectories with aligned final motions is evaluated using the same layout of target placements as Experiment 7, with the Palmar reflex enabled as in Experiment 8.

The agent concludes that the ideal approach for the Palmar reflex activation event should use matching directions for all vectors describing the motion and orientation of the hand, {g→p,g→f,m→p,f,m→p,t,m→f,t}, and all of these parallel vectors should be perpendicular to the target's major axis o→.

By choosing the best aligned candidate final node instead of the closest candidate node and then adjusting the entire final motion to match its gripper vector, the reliability of grasping is nearly tripled to 35%.

Adjusting this is analogous to a human's preshaping techniques to ready the hand for grasping an object, though simpler, as there are fewer ways to configure parallel grippers than an anthropomorphic hand.

In order to avoid new failures from introducing large, sudden rotations of the hand near the target, when a new q7 is chosen it will be used instead of the stored q7 value of all nodes in the trajectory nTj.

Over the same set of 40 object placements from previous experiments, this technique increases the number of Palmar reflex activations (Palmar bumps, weak grasps, and grasps) to 30 (75%), and grasps to 20 (50%), as shown in Figures 11, 12.

In principle, any time new successes are achieved, they can be treated as new example grasps with ideal q7 values to consider for trials with nearby target placements, allowing for further improvements to the success rate.

Tabulated Results from experiments 8, 11, and 12: We have demonstrated a computational model of an embodied learning agent, implemented on a physical Baxter robot, exploring its sensorimotor space without explicit guidance or feedback, constructing a representation of the robot's peripersonal space (the PPS graph), including a mapping between the proprioceptive sensor and the visual sensor.

This work makes several contributions to developmental learning: By unguided exploration of the proprioceptive and visual spaces, and without prior knowledge of the structure or dimensionality of either space, the learning agent can construct a graph-structured skeleton (the PPS Graph) that enables manipulator motion planning by finding and following paths within the graph.

By learning conditions to make a rare action (i.e., reaching to cause a bump of a block) reliable, the agent learns a criterion on perceptual images (stored and current) that allows it to select a suitable target node in the PPS Graph.

The PPS Graph representation accounts for reaching in a way that matches striking qualitative properties of early human infant reaching: jerky motion, and independence from vision of the hand.

By interpreting the target node and its neighborhood as a sample from a continuous space, the agent can approximate the local Jacobian of the hand pose in perceptual space with respect to the joint angles.

BK and JJ collaborated on the development of the model and the design of the study, analyzing the data, wrote sections of the manuscript, and both contributed to manuscript revision, and read and approved the submitted version.

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