To reduce the computational cost of humanoid motion generation, we introduce a new approach to representing robot kinematic reachability: the differentiable reachability map. This map is a scalar-valued function defined in the task space that takes positive values only in regions reachable by the robot's end-effector. A key feature of this representation is that it is continuous and differentiable with respect to task-space coordinates, enabling its direct use as constraints in continuous optimization for humanoid motion planning. We describe a method to learn such differentiable reachability maps from a set of end-effector poses generated using a robot's kinematic model, using either a neural network or a support vector machine as the learning model. By incorporating the learned reachability map as a constraint, we formulate humanoid motion generation as a continuous optimization problem. We demonstrate that the proposed approach efficiently solves various motion planning problems, including footstep planning, multi-contact motion planning, and loco-manipulation planning for humanoid robots.

This work was partially carried out when PM was working at the University of Trento. Figure 1 shows the various parts composing a pipe and their disposition. Notice that first two indexes describe the position, e.g. Results are obtained by evaluating a batch of 5000 generated samples.

--In this letter, we propose an efficient and highly versatile loco-manipulation planning for humanoid robots. Loco-manipulation planning is a key technological brick enabling humanoid robots to autonomously perform object transportation by manipulating them. We formulate planning of the alternation and sequencing of footsteps and grasps as a graph search problem with a new transition model that allows for a flexible representation of loco-manipulation. Our transition model is quickly evaluated by relocating and switching the reachability maps depending on the motion of both the robot and object. We evaluate our approach by applying it to loco-manipulation use-cases, such as a bobbin rolling operation with regrasping, where the motion is automatically planned by our framework. OVING large objects is a typical task required for humanoid robots in large-scale manufacturing environments. As most of such objects are heavy, they need to be moved through manipulating them by taking advantage of the ground and any possible inertia properties.

Robots are strongly expected as a means of replacing human tasks. If a robot has a human-like physicality, the possibility of replacing human tasks increases. In the case of household service robots, it is desirable for them to be on a human-like size so that they do not become excessively large in order to coexist with humans in their operating environment. However, robots with size limitations tend to have difficulty solving inverse kinematics (IK) due to mechanical limitations, such as joint angle limitations. Conversely, if the difficulty coming from this limitation could be mitigated, one can expect that the use of such robots becomes more valuable. In numerical IK solver, which is commonly used for robots with higher degrees-of-freedom (DOF), the solvability of IK depends on the initial guess given to the solver. Thus, this paper proposes a method for generating a good initial guess for a numerical IK solver given the target hand configuration. For the purpose, we define the goodness of an initial guess using the scaled Jacobian matrix, which can calculate the manipulability index considering the joint limits. These two factors are related to the difficulty of solving IK. We generate the initial guess by optimizing the goodness using the genetic algorithm (GA). To enumerate much possible IK solutions, we use the reachability map that represents the reachable area of the robot hand in the arm-base coordinate system. We conduct quantitative evaluation and prove that using an initial guess that is judged to be better using the goodness value increases the probability that IK is solved. Finally, as an application of the proposed method, we show that by generating good initial guesses for IK a robot actually achieves three typical scenarios.

Legged robots with advanced manipulation capabilities have the potential to significantly improve household duties and urban maintenance. Despite considerable progress in developing robust locomotion and precise manipulation methods, seamlessly integrating these into cohesive whole-body control for real-world applications remains challenging. In this paper, we present a modular framework for robust and generalizable whole-body loco-manipulation controller based on a single arm-mounted camera. By using reinforcement learning (RL), we enable a robust low-level policy for command execution over 5 dimensions (5D) and a grasp-aware high-level policy guided by a novel metric, Generalized Oriented Reachability Map (GORM). The proposed system achieves state-of-the-art one-time grasping accuracy of 89% in the real world, including challenging tasks such as grasping transparent objects. Through extensive simulations and real-world experiments, we demonstrate that our system can effectively manage a large workspace, from floor level to above body height, and perform diverse whole-body loco-manipulation tasks.

Knowledge of a manipulator's workspace is fundamental for a variety of tasks including robot design, grasp planning and robot base placement. Consequently, workspace representations are well studied in robotics. Two important representations are reachability maps and inverse reachability maps. The former predicts whether a given end-effector pose is reachable from where the robot currently is, and the latter suggests suitable base positions for a desired end-effector pose. Typically, the reachability map is built by discretizing the 6D space containing the robot's workspace and determining, for each cell, whether it is reachable or not. The reachability map is subsequently inverted to build the inverse map. This is a cumbersome process which restricts the applications of such maps. In this work, we exploit commonalities of existing six and seven axis robot arms to reduce the dimension of the discretization from 6D to 4D. We propose Reachability Map 4D (RM4D), a map that only requires a single 4D data structure for both forward and inverse queries. This gives a much more compact map that can be constructed by an order of magnitude faster than existing maps, with no inversion overheads and no loss in accuracy. Our experiments showcase the usefulness of RM4D for grasp planning with a mobile manipulator.

Humans coordinate the abundant degrees of freedom (DoFs) of hands to dexterously perform tasks in everyday life. We imitate human strategies to advance the dexterity of multi-DoF robotic hands. Specifically, we enable a robot hand to grasp multiple objects by exploiting its kinematic redundancy, referring to all its controllable DoFs. We propose a human-like grasp synthesis algorithm to generate grasps using pairwise contacts on arbitrary opposing hand surface regions, no longer limited to fingertips or hand inner surface. To model the available space of the hand for grasp, we construct a reachability map, consisting of reachable spaces of all finger phalanges and the palm. It guides the formulation of a constrained optimization problem, solving for feasible and stable grasps. We formulate an iterative process to empower robotic hands to grasp multiple objects in sequence. Moreover, we propose a kinematic efficiency metric and an associated strategy to facilitate exploiting kinematic redundancy. We validated our approaches by generating grasps of single and multiple objects using various hand surface regions. Such grasps can be successfully replicated on a real robotic hand.

In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of dynamical systems. By sampling inputs, evaluating their images in the true reachable set, and taking their ɛ-padded convex hull as a set estimator, this algorithm applies to general problem settings and is simple to implement. Our main contribution is the derivation of asymptotic and finite-sample accuracy guarantees using random set theory. This analysis informs algorithmic design to obtain an ɛ-close reachable set approximation with high probability, provides insights into which reachability problems are most challenging, and motivates safety-critical applications of the technique. On a neural network verification task, we show that this approach is more accurate and significantly faster than prior work. Informed by our analysis, we also design a robust model predictive controller that we demonstrate in hardware experiments. Keywords: reachability analysis, random set theory, robust control, neural network verification.