We consider time-optimal motion planning for dynamical systems that are translation-invariant, a property that holds for many mobile robots, such as differential-drives, cars, airplanes, and multirotors. Our key insight is that we can extend graph-search algorithms to the continuous case when used symbiotically with optimization. For the graph search, we introduce discontinuity-bounded A* (db-A*), a generalization of the A* algorithm that uses concepts and data structures from sampling-based planners. Db-A* reuses short trajectories, so-called motion primitives, as edges and allows a maximum user-specified discontinuity at the vertices. These trajectories are locally repaired with trajectory optimization, which also provides new improved motion primitives. Our novel kinodynamic motion planner, kMP-db-A*, has almost surely asymptotic optimal behavior and computes near-optimal solutions quickly. For our empirical validation, we provide the first benchmark that compares search-, sampling-, and optimization-based time-optimal motion planning on multiple dynamical systems in different settings. Compared to the baselines, kMP-db-A* consistently solves more problem instances, finds lower-cost initial solutions, and converges more quickly.

Resource allocation, mechanism design, load balancing, strategic classification, and many other problems with economic incentives require optimizing an objective function on the simplex. The simplex constraint can describe a fixed load to be distributed [6], a constraint on the budget to be allocated [7], or a distribution over actions individuals can take [9]; see Bomze [1] and De Klerk [3] for a survey on simplex optimization with applications. Moreover, these optimization problems often have to be solved using only zeroth-order feedback, i.e., function evaluations at different points on the simplex, as gradient feedback is not easily obtainable. There are a number of methods for zeroth-order optimization (e.g.

Multi-view clustering (MVC) optimally integrates complementary information from different views to improve clustering performance. Although demonstrating promising performance in various applications, most of existing approaches directly fuse multiple pre-specified similarities to learn an optimal similarity matrix for clustering, which could cause over-complicated optimization and intensive computational cost. In this paper, we propose late fusion MVC via alignment maximization to address these issues. To do so, we first reveal the theoretical connection of existing k-means clustering and the alignment between base partitions and the consensus one. Based on this observation, we propose a simple but effective multi-view algorithm termed LF-MVC-GAM. It optimally fuses multiple source information in partition level from each individual view, and maximally aligns the consensus partition with these weighted base ones. Such an alignment is beneficial to integrate partition level information and significantly reduce the computational complexity by sufficiently simplifying the optimization procedure. We then design another variant, LF-MVC-LAM to further improve the clustering performance by preserving the local intrinsic structure among multiple partition spaces. After that, we develop two three-step iterative algorithms to solve the resultant optimization problems with theoretically guaranteed convergence. Further, we provide the generalization error bound analysis of the proposed algorithms. Extensive experiments on eighteen multi-view benchmark datasets demonstrate the effectiveness and efficiency of the proposed LF-MVC-GAM and LF-MVC-LAM, ranging from small to large-scale data items. The codes of the proposed algorithms are publicly available at https://github.com/wangsiwei2010/latefusionalignment.

This paper proposes a hybrid learning and optimization framework for mobile manipulators for complex and physically interactive tasks. The framework exploits an admittance-type physical interface to obtain intuitive and simplified human demonstrations and Gaussian Mixture Model (GMM)/Gaussian Mixture Regression (GMR) to encode and generate the learned task requirements in terms of position, velocity, and force profiles. Next, using the desired trajectories and force profiles generated by GMM/GMR, the impedance parameters of a Cartesian impedance controller are optimized online through a Quadratic Program augmented with an energy tank to ensure the passivity of the controlled system. Two experiments are conducted to validate the framework, comparing our method with two approaches with constant stiffness (high and low). The results showed that the proposed method outperforms the other two cases in terms of trajectory tracking and generated interaction forces, even in the presence of disturbances such as unexpected end-effector collisions.

The decision-making of TBM operating parameters has an important guiding significance for TBM safe and efficient construction, and it has been one of the research hotpots in the field of TBM tunneling. For this purpose, this paper introduces rock-breaking rules into machine learning method, and a rock-machine mapping dual-driven by physical-rule and data-mining is established with high accuracy. This dual-driven mappings are subsequently used as objective function and constraints to build a decision-making method for TBM operating parameters. By searching the revolution per minute and penetration corresponding to the extremum of the objective function subject to the constraints, the optimal operating parameters can be obtained. This method is verified in the field of the Second Water Source Channel of Hangzhou, China, resulting in the average penetration rate increased by 11.3%, and the total cost decreased by 10.0%, which proves the practicability and effectiveness of the developed decision-making model.

The metaverse has the potential to revolutionize the next generation of the Internet by supporting highly interactive services with the help of Mixed Reality (MR) technologies; still, to provide a satisfactory experience for users, the synchronization between the physical world and its digital models is crucial. This work proposes a sampling, communication and prediction co-design framework to minimize the communication load subject to a constraint on tracking the Mean Squared Error (MSE) between a real-world device and its digital model in the metaverse. To optimize the sampling rate and the prediction horizon, we exploit expert knowledge and develop a constrained Deep Reinforcement Learning (DRL) algorithm, named Knowledge-assisted Constrained Twin-Delayed Deep Deterministic (KC-TD3) policy gradient algorithm. We validate our framework on a prototype composed of a real-world robotic arm and its digital model. Compared with existing approaches: (1) When the tracking error constraint is stringent (MSE=0.002 degrees), our policy degenerates into the policy in the sampling-communication co-design framework. (2) When the tracking error constraint is mild (MSE=0.007 degrees), our policy degenerates into the policy in the prediction-communication co-design framework. (3) Our framework achieves a better trade-off between the average MSE and the average communication load compared with a communication system without sampling and prediction. For example, the average communication load can be reduced up to 87% when the track error constraint is 0.002 degrees. (4) Our policy outperforms the benchmark with the static sampling rate and prediction horizon optimized by exhaustive search, in terms of the tail probability of the tracking error. Furthermore, with the assistance of expert knowledge, the proposed algorithm KC-TD3 achieves better convergence time, stability, and final policy performance.

Abstract-- In this paper we present a motion planner for LIMMS, a modular multi-agent, multi-modal package delivery platform. A single LIMMS unit is a robot that can operate as an arm or leg depending on how and what it is attached to, e.g., a manipulator when it is anchored to walls within a delivery vehicle or a quadruped robot when 4 are attached to a box. Coordinating amongst multiple LIMMS, when each one can take on vastly different roles, can quickly become complex. The formulation is then solved for skill exploration and can be implemented on hardware after refinement. To solve this optimization problem we use alternating direction method of multipliers (ADMM). The proposed planner is experimented under various scenarios which shows the capability of LIMMS to enter into different modes or combinations of them to achieve their goal of moving shipping boxes.

Recently, Stochastic Gradient Descent (SGD) and its variants have become the dominant methods in the large-scale optimization of machine learning (ML) problems. A variety of strategies have been proposed for tuning the step sizes, ranging from adaptive step sizes to heuristic methods to change the step size in each iteration. Also, momentum has been widely employed in ML tasks to accelerate the training process. Yet, there is a gap in our theoretical understanding of them. In this work, we start to close this gap by providing formal guarantees to a few heuristic optimization methods and proposing improved algorithms. First, we analyze a generalized version of the AdaGrad (Delayed AdaGrad) step sizes in both convex and non-convex settings, showing that these step sizes allow the algorithms to automatically adapt to the level of noise of the stochastic gradients. We show for the first time sufficient conditions for Delayed AdaGrad to achieve almost sure convergence of the gradients to zero. Moreover, we present a high probability analysis for Delayed AdaGrad and its momentum variant in the non-convex setting. Second, we analyze SGD with exponential and cosine step sizes, which are empirically successful but lack theoretical support. We provide the very first convergence guarantees for them in the smooth and non-convex setting, with and without the Polyak-{\L}ojasiewicz (PL) condition. We also show their good property of adaptivity to noise under the PL condition. Third, we study the last iterate of momentum methods. We prove the first lower bound in the convex setting for the last iterate of SGD with constant momentum. Moreover, we investigate a class of Follow-The-Regularized-Leader-based momentum algorithms with increasing momentum and shrinking updates. We show that their last iterate has optimal convergence for unconstrained convex stochastic optimization problems.

Robots often need to solve path planning problems where essential and discrete aspects of the environment are partially observable. This introduces a multi-modality, where the robot must be able to observe and infer the state of its environment. To tackle this problem, we introduce the Path-Tree Optimization (PTO) algorithm which plans a path-tree in belief-space. A path-tree is a tree-like motion with branching points where the robot receives an observation leading to a belief-state update. The robot takes different branches depending on the observation received. The algorithm has three main steps. First, a rapidly-exploring random graph (RRG) on the state space is grown. Second, the RRG is expanded to a belief-space graph by querying the observation model. In a third step, dynamic programming is performed on the belief-space graph to extract a path-tree. The resulting path-tree combines exploration with exploitation i.e. it balances the need for gaining knowledge about the environment with the need for reaching the goal. We demonstrate the algorithm capabilities on navigation and mobile manipulation tasks, and show its advantage over a baseline using a task and motion planning approach (TAMP) both in terms of optimality and runtime.

Walking motion planning based on Divergent Component of Motion (DCM) and Linear Inverted Pendulum Model (LIPM) is one of the alternatives that could be implemented to generate online humanoid robot gait trajectories. This algorithm requires different parameters to be adjusted. Herein, we developed a framework to attain optimal parameters to achieve a stable and energy-efficient trajectory for real robot's gait. To find the optimal trajectory, four cost functions representing energy consumption, the sum of joints velocity and applied torque at each lower limb joint of the robot, and a cost function based on the Zero Moment Point (ZMP) stability criterion were considered. Genetic algorithm was employed in the framework to optimize each of these cost functions. Although the trajectory planning was done with the help of the simplified model, the values of each cost function were obtained by considering the full dynamics model and foot-ground contact model in Bullet physics engine simulator. The results of this optimization yield that walking with the most stability and walking in the most efficient way are in contrast with each other. Therefore, in another attempt, multi-objective optimization for ZMP and energy cost functions at three different speeds was performed. Finally, we compared the designed trajectory, which was generated using optimal parameters, with the simulation results in Choreonoid simulator.